### Mathematics - Conic Sections

#### Question - 1

The equation of parabola having vertex (0, 0) passing through (2, 3) and axis is X - axis, is

• A ${ x }^{ 2 }=\frac { 9 }{ 2 } y$
• B ${ y }^{ 2 }=\frac { 9 }{ 2 } x$
• C ${ y }^{ 2 }=-\frac { 9 }{ 2 } x$
• D ${ x }^{ 2 }=-\frac { 9 }{ 2 } y$

#### Question - 2

If the points (0, 4) and (0, 2) are respectively the vertex and focus of a parabola, then the equation of the parabola is

• A ${ x }^{ 2 }+8y=16$
• B ${ x }^{ 2 }+8y=32$
• C ${ x }^{ 2 }+16y=30$
• D ${ x }^{ 2 }-8y=32$

#### Question - 3

The equation of the parabola, whose axis is parallel to Y - axis and which passes through the points (0, 4), (1, 9) and (-2, 6), is

• A $y=2\left( x+\frac { 3 }{ 4 } \right) ^{ 2 }+\frac { 23 }{ 8 }$
• B $y=2\left( x+\frac { 3 }{ 2 } \right) ^{ 2 }-\frac { 1 }{ 2 }$
• C $y=2\left( x+\frac { 3 }{ 5 } \right) ^{ 2 }+\frac { 1 }{ 2 }$
• D $y=2\left( x+\frac { 1 }{ 2 } \right) ^{ 2 }-\frac { 1 }{ 2 }$

#### Question - 4

The equation(s) of the common tangent(s) to the parabolas y2 - 4x - 2y + 5 = 0 and y2 = - 4x is/are

• A $x+y=2\\ x-y=1$
• B $x+y=3\\ x-y=2$
• C $x+y=1\\ 4x-2y-1=0$
• D $x+2y=1\\ x+y=-3$

#### Question - 5

The locus of the middle points of the chords of the parabola y2 = 4x which touch the parabola x2 = -8y is

• A ${ y }^{ 3 }-2xy-8=0$
• B ${ y }^{ 3 }+2xy-8=0$
• C ${ y }^{ 3 }-2xy+8=0$
• D ${ y }^{ 3 }-xy-8=0$

#### Question - 6

If e is the eccentricity of the ellipse $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1$ then

• A ${ b }^{ 2 }={ a }^{ 2 }(1-{ e }^{ 2 })$
• B ${ a }^{ 2 }={ b }^{ 2 }(1-{ e }^{ 2 })$
• C ${ a }^{ 2 }={ b }^{ 2 }({ e }^{ 2 }-1)$
• D ${ b }^{ 2 }={ a }^{ 2 }({ e }^{ 2 }-1)$

#### Question - 7

If P is a point on the ellipse $\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 25 } =1$ whose foci are S and S', then PS + PS' is equal to

• A 8
• B 7
• C 5
• D 10

#### Question - 8

The equation of the ellipse whose focus is (1, -1), the directrix x - y - 3 = 0 and eccentricity $\frac { 1 }{ 2 }$ is

• A ${ 7x }^{ 2 }+2xy+{ 7y }^{ 2 }-10x+10y+7=0$
• B ${ 7x }^{ 2 }+2xy+{ 7y }^{ 2 }+7=0$
• C ${ 7x }^{ 2 }+2xy+{ 7y }^{ 2 }+10x-10y-7=0$
• D None of the above

#### Question - 9

The number of points outside outside the ellipse on units major axis from which a normal (other than the X - axis) can be drawn to the ellipse is

• A 0
• B 3
• C 5
• D None of these

#### Question - 10

From the point A(4, 3), tangents are drawn to the ellipse $\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1$ to touch the ellipse at B and C. EF is a tangent to the ellipse parallel to the line BC and toward the point A. The distance of A from EF is equal to.

• A $\frac { 4\sqrt { 11 } -5 }{ 2 }$
• B $\frac { 24-4\sqrt { 18 } }{ 5 }$
• C $\frac { 24+4\sqrt { 18 } }{ 5 }$
• D $\frac { 24+2\sqrt { 11 } }{ 5 }$