NDA 2017 Paper 1 | Circle Question 10 | Mathematics

What is the equation of the circle which passes through the points (3, $$-$$2) and ($$-$$2, 0) and having its centre on the line 2x $$-$$ y $$-$$ 3 = 0 ?

x² + y² + 3x + 2 = 0

x² + y² + 3x + 12y + 2 = 0

x² + y² + 2x = 0

x² + y² = 5

NDA 2018 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

The equation of a circle whose end points of a diameter are (x₁, y₁) and (x₂, y₂) is

$$(x - {x_1})(x - {x_2}) + (y - {y_1})(y - {y_2}) = {x^2} + {y^2}$$

$${(x - {x_1})^2} + {(y - {y_1})^2} = {x_2}{y_2}$$

$${x^2} + {y^2} + 2{x_1}{x_2} + 2{y_1}{y_2} = 0$$

$$(x - {x_1})(x - {x_2}) + (y - {y_1})(y - {y_2}) = 0$$

NDA 2018 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

If Y-axis touches the circle $${x^2} + {y^2} + gx + fy + {c \over 4} = 0$$, then the normal at this point intersects the circle at the point.

$$\left( { - {g \over 2},{f \over 2}} \right)$$

$$\left( { - g, - {f \over 2}} \right)$$

$$\left( { - {g \over 2},f} \right)$$

$$\left( { - g, - f} \right)$$

NDA 2019 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

A circle is drawn on the chord of a circle x² + y² = a² as diameter. The chord lies on the line x + y = a. What is the equation of the circle?

x² + y² $$-$$ ax $$-$$ ay + a² = 0

x² + y² $$-$$ ax $$-$$ ay = 0

x² + y² + ax + ay = 0

x² + y² + ax + ay $$-$$ 2a² = 0

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