JEE Main 2013 (Offline) | Conic Sections Question 211 | Mathematics

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)

-1

The equation of the circle passing through the foci of the ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1$$, and having centre at $$(0,3)$$ is

$${x^2} + {y^2} - 6y - 7 = 0$$

$${x^2} + {y^2} - 6y + 7 = 0$$

$${x^2} + {y^2} - 6y - 5 = 0$$

$${x^2} + {y^2} - 6y + 5 = 0$$

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)

-1

Given : A circle, $$2{x^2} + 2{y^2} = 5$$ and a parabola, $${y^2} = 4\sqrt 5 x$$.
Statement-1 : An equation of a common tangent to these curves is $$y = x + \sqrt 5 $$.

Statement-2 : If the line, $$y = mx + {{\sqrt 5 } \over m}\left( {m \ne 0} \right)$$ is their common tangent, then $$m$$ satiesfies $${m^4} - 3{m^2} + 2 = 0$$.

Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Statement-1 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

Statement-1 is true; Statement-2 is false.

Statement-1 is false Statement-2 is true.

AIEEE 2012

MCQ (Single Correct Answer)

-1

STATEMENT-1 : An equation of a common tangent to the parabola $${y^2} = 16\sqrt 3 x$$ and the ellipse $$2{x^2} + {y^2} = 4$$ is $$y = 2x + 2\sqrt 3 $$

STATEMENT-2 :If line $$y = mx + {{4\sqrt 3 } \over m},\left( {m \ne 0} \right)$$ is a common tangent to the parabola $${y^2} = 16\sqrt {3x} $$and the ellipse $$2{x^2} + {y^2} = 4$$, then $$m$$ satisfies $${m^4} + 2{m^2} = 24$$

Statement-1 is false, Statement-2 is true.

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

Statement-1 is true, Statement-2 is false.

AIEEE 2012

MCQ (Single Correct Answer)

-1

An ellipse is drawn by taking a diameter of thec circle $${\left( {x - 1} \right)^2} + {y^2} = 1$$ as its semi-minor axis and a diameter of the circle $${x^2} + {\left( {y - 2} \right)^2} = 4$$ is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is:

$$4{x^2} + {y^2} = 4$$

$${x^2} + 4{y^2} = 8$$

$$4{x^2} + {y^2} = 8$$

$${x^2} + 4{y^2} = 16$$

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