Parabola

Q.

AB is a chord of the parabola $y^2=4ax$ with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. the projection of BC on the x-axis is ka. What's the value of 'k'?

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Q.

The points on the parabola $y^2=12x$ whose focal distance is 4 , are

1. 

2. None of these

3. 

4. (1, 2)

Q.

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and $100m$ long is supported by vertical wires attached to the cable, the longest wire being $30m$ and the shortest being 6 m. Find the length of a supporting wire attached to the roadway $18m$ from the middle.

Q.

Find the equation of the hyperbola with foci (0, $\pm$ 3) and vertices $(0,\pm \frac{\sqrt{11}}{2})$.

Q.

The equation of the lines joining the vertex of the parabola $y^2=6x$ to the point on it whose abscissa is 24 , is

1. 

2. 

3. 

4. 

Q. The equation of the parabola whose focus is $(4,-3)$ and vertex is $(4,-1)$

1. $x^2-8x+8y+24=0$
2. $x^2-8x-8y+8=0$
3. $x^2-8x+8y+8=0$
4. $x^2-8x+8y+32=0$

Q.

Any point on the parabola whose focus is (0, 1) and the directrix is x+2=0 is given by

1. $t^2+1,2t-1$

2. $t^2+1,2t+1$

3. $t^2,2t$

4. $t^2-1,2t+1$

Q. The locus of the mid-point of the line segment joining the focus to a moving point on the parabola $y^2=4ax$ is another parabola with directrix

1. $x=-a$
2. $x=-\frac{a}{2}$
3. $x=0$
4. $x=\frac{a}{2}$

Q. The equation of the parabola whose focus is $(-6,-6)$ and vertex is $(-2,2),$ is

1. $(2x-y{)}^2+104x+148y-124=0$
2. $(2x-y{)}^2+104x-148y+124=0$
3. $(2x-y{)}^2-104x+148y+124=0$
4. $(2x+y{)}^2+104x+148y-124=0$

Q. The area of the triangle formed by the intersection of a line parallel to x-axis and passing through $P(h,k)$ with the lines $y=x$ and $x+y=12$ is $4h^2$. If the locus of the point $P$ is $y=\pm Px+Q$, then the value of $P+Q$ is

Q. If the equation $\sqrt{(x-1{)}^2+(y-2{)}^2}=\sqrt{\lambda }|x+y+3|$ represents a parabola, then

1. $\lambda =1$
2. $\lambda =\frac{1}{3}$
3. Coordinates of focus are $(1,2)$
4. Coordinates of focus are $(1,0)$