### Mathematics - Coordinate Geometry - II

#### Question - 1

The equation of the parabola having vertex at(0,1) and the focus at(0,0), is

• A $x^2=4(y-1)$
• B $x^2=-4(y-1)$
• C $x^2=4(y+1)$
• D $x^2=-4(y+1)$

#### Question - 2

The equation of the parabola having vertex at(a,0) and focus at (a,0) is

• A y2=4(a'-a)x
• B y2=4(a'-a)(x-a')
• C y2=4(a'-a)(x-a)
• D None of these

#### Question - 3

The equation of parabola whose focus is(-8,-2) and the directrix is 2x-y-9=0

• A $x^2-4xy+4y^2+116x+2y+259=0$
• B $x^2+4xy+y^2+116x+2y+259=0$
• C $x^2+4xy+4y^2-116x+2y+259=0$
• D $x^2-4xy+4y^2+116x-2y+259=0$

#### Question - 4

The coordinates of the vertex and focus of the parabola $y^2-8y-x+19=0$are respectively

• A $_{ }(3,4),\left( \frac { 13 }{ 4 } ,4 \right)$
• B $_{ }(-3,-4),\left( \frac { 13 }{ 4 } ,4 \right)$
• C $_{ }(3,4),\left( \frac { -13 }{ 4 } ,-4 \right)$
• D None of these

#### Question - 5

The equation of the matrix of the parabola$y^2+4y+4x+2=0$ is

• A x=-1
• B x=1
• C $x=-\frac { 3 }{ 2 }$
• D $x=\frac { 3 }{ 2 }$

#### Question - 6

If y1,y2,y3 are the ordinates of the verticles of triangle inscribed in parabola y2=4ax, then area of the triangle, is

• A $\frac { 1 }{ 2a } |(y1-y)(y2-y3)(y3-y1)|$
• B $\frac { 1 }{ 4a } |(y1-y)(y2-y3)(y3-y1)|$
• C $\frac { 1 }{ 8a } |(y1-y)(y2-y3)(y3-y1)|$
• D $\frac { 1 }{ 16a } |(y1-y)(y2-y3)(y3-y1)|$

#### Question - 7

The curved is represented by the parametric equations x=t2+t+1,y=t2-t+1 is

• A a pair of straight lines
• B a circle
• C a parabola
• D an ellipse

#### Question - 8

If the line x-1=0,is the directrix of the parabola y2-kx+8=0,then one of the value of k is

• A $1\over8$
• B 8
• C $1\over4$
• D 4

#### Question - 9

If the vertex of a parabola is(-5,0) and directrix of the line x+3=0 then equation of the parabola,is

• A y2=4x+16
• B y2=-4x+16
• C y2=4x-16
• D None of these

#### Question - 10

If lengths of the focal chord segments of the parabola y2=4ax are l1 and l2,then length of the latus rectrum is

• A $l1+l2\over2$
• B $4 l1l2\over l1+l2$
• C $2 l1l2\over l1+l2$
• D $\sqrt { l1l2 }$