### Mathematics - Coordinate Geometry - II

#### Question - 1

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 - 2

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 - 3

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 - 4

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 - 5

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 - 6

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 - 7

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 $\sqrt { l1l2 }$

#### Question - 8

The coordinates of the points on the parabola y2=16x whose focal ditance is 8 units,are

• A $(4,\pm8)$
• B $(2,\pm4\sqrt { 2 } )$
• C $(6,\pm4\sqrt { 6 } )$
• D None of these

#### Question - 9

The coordinates of the point of intersection of tangents at the points(x1,y1) and (x2,y2)  on the parabola is (x3,y3);then y1,y2,y3 are in

• A A.P
• B G.P
• C H.P
• D None of these

#### Question - 10

The coordinates of the focus of the parabola y2=8x are

• A (2,0)
• B (-2,0)
• C (0,2)
• D (0.-2)