Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
If the lines 3x − 4y + 4 = 0 and 6x − 8y − 7 = 0 are tangents to a circle, then find the radius of the circle
पर्याय
`3/4`
`4/3`
`1/4`
`7/4`
Advertisements
उत्तर
`3/4`
Explanation;
Tangents are parallel to each other.
∴ Perpendicular distance between tangents = diameter
∴ `|(4 - (-7/2))/sqrt(3^2 + (-4)^2)|` = 2r
∴ `(15/2)/5` = 2r
∴ r = `3/4`.
APPEARS IN
संबंधित प्रश्न
Find the equation of the circle with centre at origin and radius 4.
Find the equation of the circle with centre at (2, −3) and radius 5.
Find the centre and radius of the circle:
x2 + y2 = 25
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 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
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 − 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
Choose the correct alternative:
If a circle passes through the point (0, 0), (a, 0) and (0, b) then find the co-ordinates of its centre
Choose the correct alternative:
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
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
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.
Answer the following :
Find the equation of the circle concentric with x2 + y2 – 4x + 6y = 1 and having radius 4 units
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 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 :
Find the length of the tangent segment drawn from the point (5, 3) to the circle x2 + y2 + 10x – 6y – 17 = 0
If 2x - 4y = 9 and 6x - 12y + 7 = 0 are the tangents of same circle, then its radius will be ______
If one of the diameters of the curve x2 + y2 - 4x - 6y + 9 = 0 is a chord of a circle with centre (1, 1), then the radius of this circle is ______
The centre of the circle x = 3 + 5 cos θ, y = - 4 + 5 sin θ, is ______
The equation of circle whose diameter is the line joining the points (–5, 3) and (13, –3) is ______.
The equation of a circle with centre at (1, 0) and circumference 10π units is ______.
The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines x² − y² − 2x + 4y − 3 = 0 is
