JEE Main 2022 (Online) 26th June Morning Shift | Circle Question 54 | Mathematics

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 :

$${{65} \over 2}$$

$${{61} \over 2}$$

JEE Main 2022 (Online) 25th June Evening Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

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

$$y = \sqrt 2 x$$

$$x = \sqrt 2 y$$

$${y^2} - {x^2} = 2xy$$

$${x^2} - {y^2} = 2xy$$

JEE Main 2022 (Online) 25th June Morning Shift

MCQ (Single Correct Answer)

-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 :

$${(x - 1)^2} + {(y - 2)^2} = 4$$

$${(x + 1)^2} + {(y - 2)^2} = 4$$

$${(x - 1)^2} + {(y + 2)^2} = 16$$

$${(x - 1)^2} + {(y - 2)^2} = 16$$

JEE Main 2021 (Online) 27th August Evening Shift

MCQ (Single Correct Answer)

-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 2^p, then the value of p is :