Question

For what value of k will (k – 5)x²+ 2ky²-5x + 6y – 3 = 0 represents a circle?​

Answer 1

Given,

Equation of circle (k-5)x²+2ky²-5x+6y-3 = 0

To Find,

Value of k

Solution,

In the equation of circle, the coefficient of x² is always equal to the coefficient of y².

Therefore,

(k-5) = 2k

k=-5

Hence, the value of k is -5.

Answer 2

Given:

(k – 5)x²+ 2ky²-5x + 6y – 3 = 0 represents a circle

To Find:

Value of k

Solution:

In the equation of circle, the coefficient of x² is always equal to the coefficient of y².

Here,

Coefficient of x² = k-5

Coefficient of y² = 2k

Therefore, equating both we get

Coefficient of x² = Coefficient of y²

⇒(k-5) = 2k

        k = -5

Hence, the value of k is -5.