Question

The locus of centre of circle of radius 2 units, if intercept cut on x-axis by circle is twice of intercept on y-axis is

• A. 4x² –3y² = 4
• B. 4x² –y² = 12
• C. 4y² –x² = 12
• D. 4y² –3x² = 4

Answer 1

Answer: (B)

4x² –y² = 12

Answer 2

Let (h, k) is centre of circle

\Intercept on x-axis = 2$\sqrt{h^{2} - c}$

Intercept on y- axis = 2$\sqrt{k^{2} - c}$

\ $\sqrt{h^{2} - c}$= 2$\sqrt{k^{2} - c}$

h² – 4k² = – 3c … (1)

Now radius = 2

h² + k² – c = 4 … (2)

from (1) and (2)

4x² – y² = 12