IIT-JEE 2010 Paper 1 Offline | Conic Sections Question 47 | Mathematics

IIT-JEE 2010 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

Let $$A$$ and $$B$$ be two distinct points on the parabola $${y^2} = 4x$$. If the axis of the parabola touches a circle of radius $$r$$ having $$AB$$ as its diameter, then the slope of the line joining $$A$$ and $$B$$ can be

$$ - {1 \over r}$$

$$ {1 \over r}$$

$$ {2 \over r}$$

$$ - {2 \over r}$$

IIT-JEE 2009 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

The tangent $$PT$$ and the normal $$PN$$ to the parabola $${y^2} = 4ax$$ at a point $$P$$ on it meet its axis at points $$T$$ and $$N$$, respectively. The locus of the centroid of the triangle $$PTN$$ is a parabola whose

vertex is $$\left( {{{2a} \over 3},0} \right)$$

directrix is $$x=0$$

latus rectum is $${{{2a} \over 3}}$$

focus is $$(a, 0)$$

IIT-JEE 2009 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

An ellipse intersects the hyperbola $$2{x^2} - 2{y^2} = 1$$ orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes then

equation of ellipse is $${x^2} + 2{y^2} = 2$$

the foci of ellipse are $$\left( { \pm 1,0} \right)$$

equation of ellipse is $${x^2} + 2{y^2} = 4$$

the foci of ellipse are $$\left( { \pm \sqrt 2 ,0} \right)$$

IIT-JEE 2009 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

In a triangle $$ABC$$ with fixed base $$BC$$, the vertex $$A$$ moves such that $$$\cos \,B + \cos \,C = 4{\sin ^2}{A \over 2}.$$$

If $$a, b$$ and $$c$$ denote the lengths of the sides of the triangle opposite to the angles $$A, B$$ and $$C$$, respectively, then

$$b+c=4a$$

$$b+c=2a$$

locus of point $$A$$ is an ellipse