WB JEE 2022 | Circle Question 16 | Mathematics

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

If the equation of one tangent to the circle with centre at (2, $$-$$1) from the origin is 3x + y = 0, then the equation of the other tangent through the origin is

$$3x - y = 0$$

$$x + 3y = 0$$

$$x - 3y = 0$$

$$x + 2y = 0$$

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)

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