1
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

If the tangents drawn at the points $$O(0,0)$$ and $$P\left( {1 + \sqrt 5 ,2} \right)$$ on the circle $${x^2} + {y^2} - 2x - 4y = 0$$ intersect at the point Q, then the area of the triangle OPQ is equal to

A
$${{3 + \sqrt 5 } \over 2}$$
B
$${{4 + 2\sqrt 5 } \over 2}$$
C
$${{5 + 3\sqrt 5 } \over 2}$$
D
$${{7 + 3\sqrt 5 } \over 2}$$
2
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

The set of values of k, for which the circle $$C:4{x^2} + 4{y^2} - 12x + 8y + k = 0$$ lies inside the fourth quadrant and the point $$\left( {1, - {1 \over 3}} \right)$$ lies on or inside the circle C, is

A
an empty set
B
$$\left( {6,{{65} \over 9}} \right]$$
C
$$\left[ {{{80} \over 9},10} \right)$$
D
$$\left( {9,{{92} \over 9}} \right]$$
3
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

Let C be a circle passing through the points A(2, $$-$$1) and B(3, 4). The line segment AB s not a diameter of C. If r is the radius of C and its centre lies on the circle $${(x - 5)^2} + {(y - 1)^2} = {{13} \over 2}$$, then r2 is equal to:

A
32
B
$${{65} \over 2}$$
C
$${{61} \over 2}$$
D
30
4
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is :

A
$$y = \sqrt 2 x$$
B
$$x = \sqrt 2 y$$
C
$${y^2} - {x^2} = 2xy$$
D
$${x^2} - {y^2} = 2xy$$
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