NDA 1 2025 Maths, question 56

Topic: Analytical geometry

Q56

What is the equation of the circle whose diameter is 10 cm and the equations of two of its diameters are $x + y = 0$ and $x - y = 0$ ?

(a) $x^{2} + y^{2} = 1$
(b) $x^{2} + y^{2} = 25$ Correct answer
(c) $x^{2} + y^{2} = 100$
(d) $x^{2} + y^{2} - 2x - 2y - 23 = 0$

Solution.

Answer: (b) $x^{2} + y^{2} = 25$

The centre is the intersection of the two diameter lines.
Solving $x + y = 0$ and $x - y = 0$ gives $(0,0)$ .
The radius is $10/2 = 5$ cm, so the equation is $x^{2} + y^{2} = 25$ .