1
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1
Out of Syllabus

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
$${x^2} - {y^2} = 2xy$$
2
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1
Out of Syllabus
Let a circle C touch the lines $${L_1}:4x - 3y + {K_1} = 0$$ and $${L_2} = 4x - 3y + {K_2} = 0$$, $${K_1},{K_2} \in R$$. If a line passing through the centre of the circle C intersects L1 at $$( - 1,2)$$ and L2 at $$(3, - 6)$$, then the equation of the circle C is :
A
$${(x - 1)^2} + {(y - 2)^2} = 4$$
B
$${(x + 1)^2} + {(y - 2)^2} = 4$$
C
$${(x - 1)^2} + {(y + 2)^2} = 16$$
D
$${(x - 1)^2} + {(y - 2)^2} = 16$$
3
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
Let Z be the set of all integers,

$$A = \{ (x,y) \in Z \times Z:{(x - 2)^2} + {y^2} \le 4\}$$

$$B = \{ (x,y) \in Z \times Z:{x^2} + {y^2} \le 4\}$$

$$C = \{ (x,y) \in Z \times Z:{(x - 2)^2} + {(y - 2)^2} \le 4\}$$

If the total number of relation from A $$\cap$$ B to A $$\cap$$ C is 2p, then the value of p is :
A
16
B
25
C
49
D
9
4
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
A circle C touches the line x = 2y at the point (2, 1) and intersects the circle

C1 : x2 + y2 + 2y $$-$$ 5 = 0 at two points P and Q such that PQ is a diameter of C1. Then the diameter of C is :
A
$$7\sqrt 5$$
B
15
C
$$\sqrt {285}$$
D
$$4\sqrt {15}$$
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