﻿ Show that the locus of the point, the powers of which with respect to two given circles are equal, is a straight line. : Kaysons Education

# Show That The Locus Of The Point, The Powers Of Which With Respect To Two Given Circles Are Equal, Is A Straight Line.

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#### SIMILAR QUESTIONS

Q1

Show that the line 3x – 4y = 1 touches the circle x2 + y2 – 2x + 4y + 1 = 0. Find the co-ordinates of the point of contact.

Q2

The line (x – 2) cos θ + (y – 2) sin θ = 1 touches a circle for all values of θ. Find the circle.

Q3

Find the equation of the normal to the circle

x2 + y2 – 5x + 2y – 48 = 0 at the point (5, 6).

Q4

Find the equation of the tangents to the circle x2 + y2 = 16 drawn from the point (1, 4).

Q5

The angle between a pair of tangents from a point P to the circle x2 + y2+ 4x – 6y + 9 sin2α + 13 cos2α = 0 is 2α. Find the equation of the locus of the point P.

Q6

Find the length of the tangents drawn from the point (3, – 4) to the circle 2x2 + 2y2 – 7x – 9y – 13 = 0.

Q7

Find the area of the triangle formed by tangents from the point (4, 3) to the circle x2 + y2 = 9 and the line segment joining their points of contact is

Q8

Find the length of the tangent from any point on the circle x2 + y2 + 2gx+ 2fy + c = 0 to the circle x2 + y2 + 2gx + 2fy + c1 = 0 is

Q9

Find the power of point (2, 4) with respect to the circle

x2 + y2 – 6x + 4y – 8 = 0

Q10

Find the condition that chord of contact of any external point

(hk) to the circle x2 + y2 = a2 should subtend right angle at the centre of the circle.