## Question

Find the length of intercept on the S.L. 4*x* – 3*y* – 10 = 0 by the circle *x*^{2}+ *y*^{2} – 2*x* + 4*y* – 20 = 0.

### Solution

10

Centre and radius of the circle *x*^{2} + *y*^{2} – 2*x* + 4*y* – 20 = 0 are

(1, –2) and respectively.

Let OM be the perpendicular from O on the line 4*x* – 3*y* – 10 = 0

Hence line 4*x* – 3*y* – 10 = 0 passes through the centre of the circle.

Hence intercepted length = Diameter of the circle

= 2 × 5 = 10

#### SIMILAR QUESTIONS

Find the equation of the circle which passes through the points (4, 1), (6, 5) and has its centre on the line 4*x* + *y* = 16.

Find the equation of circle passing through the three non-collinear points (1, 1), (2, –1) and (3, 2).

Find the equation of the circle whose diameter is the line joining the points (–4, 3) and (12, –1). Find also the intercept made by it on *y* axis.

Find the equation of circle which touches axis of *y* at a distance 4 units from the origin and cuts the intercept of 6 units from the axis of *x*.

Equation of circle in intercepts

Find the equation of the circle which passes through the origin and makes intercepts of length *a* and *b* on axis of *x* and *y* respectively.

A circle of radius 2 lies in the first quadrant and touches both the axes of coordinate. Find the equation of circle with centre at (6, 5) and touching the above circle externally.

A circle of radius 5 units touches the coordinates axes in 1^{st} quadrant. If the circle makes one complete roll on *x* axis along positive direction of *x*axis. Find the equation in new position.

Discus the position of the points (1, 2) and (6, 0) with respect to the circle.

*x*^{2} + *y*^{2} – 4*x* + 2*y* – 11 = 0

Find the shortest and largest distance from the point (2, –7) to the circle

*x*^{2} + *y*^{2} – 14*x* – 10*y* – 151 = 0

Find the coordinates of the middle point of the chord which the circle *x*^{2}+ *y*^{2} + 4*x* – 2*y* – 3 = 0 cut off the line *x* – *y* + 2 = 0.