1
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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

A
$${x^2} + {y^2} + 2ax\sin \alpha + {a^2}\cos \alpha = 0$$
B
$${x^2} + {y^2} - 2ax - 2ay\cot \alpha = 0$$
C
$${x^2} + {y^2} - 2ax\cos \alpha - {a^2} = 0$$
D
$${x^2} + {y^2} - ax\sin \alpha - ay\cos \alpha = 0$$
2
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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

A
$${S_1} - {S_2} = 0$$
B
$${S_1} + {S_2} = 0$$
C
$${S_1} - p{S_2} = 0$$
D
$${S_1} + p{S_2} = 0$$
3
WB JEE 2022
MCQ (Single Correct Answer)
+2
-0.5
Change Language

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

A
m(m + n)
B
m + n
C
n(m + n)
D
$${1 \over 2}$$(m + n)
4
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
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
A
$$4\sqrt 3 $$ sq. units
B
$$2\sqrt 3 $$ sq. units
C
$$\sqrt 3 $$ sq. units
D
$$3\sqrt 3 $$ sq. units
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