WB JEE 2022 | Circle Question 17 | Mathematics

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

The side AB of $$\Delta$$ABC is fixed and is of length 2a unit. The vertex moves in the plane such that the vertical angle is always constant and is $$\alpha$$. Let x-axis be along AB and the origin be at A. Then the locus of the vertex is

$${x^2} + {y^2} + 2ax\sin \alpha + {a^2}\cos \alpha = 0$$

$${x^2} + {y^2} - 2ax - 2ay\cot \alpha = 0$$

$${x^2} + {y^2} - 2ax\cos \alpha - {a^2} = 0$$

$${x^2} + {y^2} - ax\sin \alpha - ay\cos \alpha = 0$$

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

Two circles $${S_1} = p{x^2} + p{y^2} + 2g'x + 2f'y + d = 0$$ and $${S_2} = {x^2} + {y^2} + 2gx + 2fy + d' = 0$$ have a common chord PQ. The equation of PQ is

$${S_1} - {S_2} = 0$$

$${S_1} + {S_2} = 0$$

$${S_1} - p{S_2} = 0$$

$${S_1} + p{S_2} = 0$$

WB JEE 2022

MCQ (Single Correct Answer)

-0.5

A straight line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB, O being the origin. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is

m(m + n)

m + n

n(m + n)

$${1 \over 2}$$(m + n)

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

Two tangents to the circle x² + y² = 4 at the points A and B meet at M($$-$$4, 0). The area of the quadrilateral MAOB, where O is the origin is

$$4\sqrt 3 $$ sq. units

$$2\sqrt 3 $$ sq. units

$$\sqrt 3 $$ sq. units

$$3\sqrt 3 $$ sq. units

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