Balbharati solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स १ (आर्ट्स अँड सायन्स) [इंग्रजी] इयत्ता ११ महाराष्ट्र राज्य मंडळ chapter 6 - Circle [Latest edition]

Find the equation of the circle with centre at origin and radius 4.

Find the equation of the circle with centre at (−3, −2) and radius 6.

Find the equation of the circle with centre at (2, −3) and radius 5.

Find the equation of the circle with centre at (−3, −3) passing through the point (−3, −6)

Find the centre and radius of the circle:

x² + y² = 25

Find the centre and radius of the circle:

(x − 5)² + (y − 3)² = 20

Find the centre and radius of the circle:

`(x - 1/2)^2 + (y + 1/3)^2 = 1/36`

Find the equation of the circle with centre at (a, b) touching the Y-axis

Find the equation of the circle with centre at (–2, 3) touching the X-axis.

Find the equation of the circle with centre on the X-axis and passing through the origin having radius 4.

Find the equation of the circle with centre at (3,1) and touching the line 8x − 15y + 25 = 0

Find the equation circle if the equations of two diameters are 2x + y = 6 and 3x + 2y = 4. When radius of circle is 9

If y = 2x is a chord of circle x² + y²−10x = 0, find the equation of circle with this chord as diametre

Find the equation of a circle with radius 4 units and touching both the co-ordinate axes having centre in third quadrant.

Find the equation of circle (a) passing through the origin and having intercepts 4 and −5 on the co-ordinate axes

Find the equation of a circle passing through the points (1,−4), (5,2) and having its centre on the line x − 2y + 9 = 0

Find the centre and radius of the following:

x² + y² − 2x + 4y − 4 = 0

Find the centre and radius of the following:

x² + y² − 6x − 8y − 24 = 0

Find the centre and radius of the following:

4x² + 4y² − 24x − 8y − 24 = 0

Show that the equation 3x² + 3y² + 12x + 18y − 11 = 0 represents a circle

Find the equation of the circle passing through the points (5, 7), (6, 6) and (2, −2)

Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic

Write the parametric equations of the circle: 

x² + y² = 9

Write the parametric equations of the circle: 

x² + y² + 2x − 4y − 4 = 0

Write the parametric equations of the circle:

(x − 3)² + (y + 4)² = 25

Find the parametric representation of the circle:

3x² + 3y² − 4x + 6y − 4 = 0

Find the equation of a tangent to the circle x² + y² − 3x + 2y = 0 at the origin

Show that the line 7x − 3y − 1 = 0 touches the circle x² + y² + 5x − 7y + 4 = 0 at point (1, 2)

Find the equation of tangent to the circle x² + y² − 4x + 3y + 2 = 0 at the point (4, −2)

Choose the correct alternative:

Equation of a circle which passes through (3, 6) and touches the axes is ______.

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If the lines 2x − 3y = 5 and 3x − 4y = 7 are the diameters of a circle of area 154 sq. units, then find the equation of the circle

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Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y − 4x + 3 = 0

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The equation of the tangent to the circle x² + y² = 4 which are parallel to x + 2y + 3 = 0 are

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If the lines 3x − 4y + 4 = 0 and 6x − 8y − 7 = 0 are tangents to a circle, then find the radius of the circle

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Area of the circle centre at (1, 2) and passing through (4, 6) is

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If a circle passes through the point (0, 0), (a, 0) and (0, b) then find the co-ordinates of its centre

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The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is

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A pair of tangents are drawn to a unit circle with center at the origin and these tangents intersect at A enclosing an angle of 60°. The area enclosed by these tangents and the area of the circle is

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The parametric equations of the circle x² + y² + mx + my = 0 are

Answer the following :

Find the centre and radius of the circle x² + y² − x +2y − 3 = 0

Answer the following :

Find the centre and radius of the circle x = 3 – 4 sinθ, y = 2 – 4cosθ

Answer the following :

Find the equation of circle passing through the point of intersection of the lines x + 3y = 0 and 2x − 7y = 0 whose centre is the point of intersection of lines x + y + 1 = 0 and x − 2y + 4 = 0

Answer the following :

Find the equation of circle which passes through the origin and cuts of chords of length 4 and 6 on the positive side of x-axis and y-axis respectively

Answer the following :

Show that the points (9, 1), (7, 9), (−2, 12) and (6, 10) are concyclic

The line 2x − y + 6 = 0 meets the circle x² + y² + 10x + 9 = 0 at A and B. Find the equation of circle on AB as diameter.

Show that x = −1 is a tangent to circle x² + y² − 2y = 0 at (−1, 1).

Answer the following :

Find the equation of tangent to the circle x² + y² = 64 at the point `"P"((2pi)/3)`

Answer the following:

Find the equation of locus of the point of intersection of perpendicular tangents drawn to the circle x = 5 cos θ and y = 5 sin θ

Answer the following :

Find the equation of the circle concentric with x² + y² – 4x + 6y = 1 and having radius 4 units

Answer the following :

Find the lengths of the intercepts made on the co-ordinate axes, by the circle:

x² + y² – 8x + y – 20 = 0

Answer the following :

Find the lengths of the intercepts made on the co-ordinate axes, by the circle:

x² + y² – 5x + 13y – 14 = 0

Answer the following :

Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:

x² + y² – 4x + 10y +20 = 0,

x² + y² + 8x – 6y – 24 = 0.

Answer the following :

Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:

x² + y² – 4x – 10y + 19 = 0,

x² + y² + 2x + 8y – 23 = 0.

Answer the following :

Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent:

x² + y² – 4x – 4y – 28 = 0,

x² + y² – 4x – 12 = 0

Answer the following :

Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent:

x² + y² + 4x – 12y + 4 = 0,

x² + y² – 2x – 4y + 4 = 0

Answer the following :

Find the length of the tangent segment drawn from the point (5, 3) to the circle x² + y² + 10x – 6y – 17 = 0

Answer the following :

Find the value of k, if the length of the tangent segment from the point (8, –3) to the circle

x² + y² – 2x + ky – 23 = 0 is `sqrt(10)`

Answer the following :

Find the equation of tangent to Circle x² + y² – 6x – 4y = 0, at the point (6, 4) on it

Answer the following :

Find the equation of tangent to Circle x² + y² = 5, at the point (1, –2) on it

Answer the following :

Find the equation of the tangent to Circle x = 5 cosθ. y = 5 sinθ, at the point θ = `pi/3` on it

Answer the following :

Show that 2x + y + 6 = 0 is a tangent to x² + y² + 2x – 2y – 3 = 0. Find its point of contact

Answer the following :

If the tangent at (3, –4) to the circle x² + y² = 25 touches the circle x² + y² + 8x – 4y + c = 0, find c

Answer the following :

Find the equations of the tangents to the circle x² + y² = 16 with slope –2

Answer the following :

Find the equations of the tangents to the circle x² + y² = 4 which are parallel to 3x + 2y + 1 = 0

Answer the following :

Find the equations of the tangents to the circle x² + y² = 36 which are perpendicular to the line 5x + y = 2

Answer the following :

Find the equations of the tangents to the circle x² + y² – 2x + 8y – 23 = 0 having slope 3

Answer the following :

Find the equation of the locus of a point, the tangents from which to the circle x² + y² = 9 are at right angles.

Answer the following :

Tangents to the circle x² + y² = a² with inclinations, θ₁ and θ₂ intersect in P. Find the locus of such that tan θ₁ + tan θ₂ = 0

Answer the following :

Tangents to the circle x² + y² = a² with inclinations, θ₁ and θ₂ intersect in P. Find the locus of such that cot θ₁ + cot θ₂ = 5

Answer the following :

Tangents to the circle x² + y² = a² with inclinations, θ₁ and θ₂ intersect in P. Find the locus of such that cot θ₁ . cot θ₂ = c