JEE Main 2022 (Online) 27th June Evening Shift | Circle Question 56 | Mathematics

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 :

an empty set

$$\left( {6,{{65} \over 9}} \right]$$

$$\left[ {{{80} \over 9},10} \right)$$

$$\left( {9,{{92} \over 9}} \right]$$

JEE Main 2022 (Online) 26th June Morning Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

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 :

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

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

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

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

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