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Question

Question: The pair of straight line joining the origin to the points of intersection of the line y = \(2\sqrt{...

The pair of straight line joining the origin to the points of intersection of the line y = 222\sqrt{2}x + c and the circle

x2 + y2 = 2 are at right angles, if-

A

c2 – 9 = 0

B

c2 – 10 = 0

C

c2 – 4 = 0

D

c2 – 8 = c

Answer

c2 – 9 = 0

Explanation

Solution

By homogenizing the equation of lines joining

origin and points of intersection of line

y = 222\sqrt{2}x + c with the circle x2 + y2 = 2 is

x2 + y2 = 2 (y22xc)2\left( \frac{y - 2\sqrt{2}x}{c} \right)^{2}

for perpendicular lines coefficient of x2 + coefficient of y2 = 0

1 – 16c2\frac{16}{c^{2}}+ 1 – 2c2\frac{2}{c^{2}}= 0

c2 – 9 = 0

c2 = 9