Advertisements
Advertisements
Question
Find the equation of circle (a) passing through the origin and having intercepts 4 and −5 on the co-ordinate axes
Advertisements
Solution
Since the circle passes through the origin and having intercepts 4 and – 5 on the coordinate axes, the circle cuts the X-axis at A(4, 0) and Y-axis at B(0, – 5).
∴ ∠AOB is a right angle.
∴ seg AB is a diameter of the circle.
∴ by diameter form, the equation of the circle is
(x – 4)(x – 0) + (y – 0)(y + 5) = 0
∴ x2 – 4x + y2 + 5y = 0
∴ x2 + y2 – 4x + 5y = 0.
APPEARS IN
RELATED QUESTIONS
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:
`(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 on the X-axis and passing through the origin having radius 4.
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 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
Show that the equation 3x2 + 3y2 + 12x + 18y − 11 = 0 represents a circle
Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic
Choose the correct alternative:
Equation of a circle which passes through (3, 6) and touches the axes is ______.
Choose the correct alternative:
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
Choose the correct alternative:
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
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
Choose the correct alternative:
Area of the circle centre at (1, 2) and passing through (4, 6) is
Answer the following :
Find the centre and radius of the circle x2 + y2 − x +2y − 3 = 0
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 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
The centre of the circle x = 3 + 5 cos θ, y = - 4 + 5 sin θ, is ______
The radius of a circle is increasing uniformly at the rate of 2.5cm/sec. The rate of increase in the area when the radius is 12cm, will be ______
If x2 + (2h - 1)xy + y2 - 24x - 8y + k = 0 is the equation of the circle and 12 is the radius of the circle, then ______.
The equation of the circle with centre (4, 5) which passes through (7, 3) 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
