Question

Locus of the centre of the circle touching the angle bisectors between the pair of lines ax² + ay² + bxy = 0

(wherea, b О R) is-

• A. xy = 0
• B. x² – y² = 0
• C. x² – y² = 1
• D. None

Answer 1

Answer: (A)

xy = 0

Answer 2

ax² + ay² + bxy = 0 ; equation of bisector

$\frac{(x^{2} - y^{2})}{a - b}$= $\frac{xy}{h}$;

h (x² – y²) = (xy) (a –b) Ю x² – y² = 0

Circle touch the lines representing bisector

In all cases one coordinate of centre of circle will be zero.

h Ч k = 0, x Ч y = 0.