Equation of Normal When Slope Is Given

Q.

Given slope m, find the equation of normal having slope m to the parabola $y^2=4ax$

1. 

2. 

3. 

4. 

Q.

For what value of k does the equation $12x^2-10xy+2y^2+11x-5y+k=0$ represents a pair of straight lines?

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Q. Find the equation of the hyperbola satisfying the give conditions: Foci $(0,\pm \sqrt{10})$
passing through $(2,3)$

Q. The equation of the line of the shortest distance between the parabola $y^2=4x$ and the circle $x^2+y^2-4x-2y+4=0$

1. x+y=3
2. x-y=3
3. 2x+y=5
4. done

Q. The equation of the normals at the end points of the latus rectum of the parabola $y^2=8x$ is/are

1. $x+y+6=0$
2. $x-y+6=0$
3. $x-y-6=0$
4. $x+y-6=0$

Q. If the normal at the point $P(a{p}^2,2ap)$ meets the parabola at $Q(a{q}^2,2aq)$ such that the lines joining the origin to $P$ and $Q$ are at right angle, then

1. $p^2=2$
2. $pq-4=0$
3. $pq+4=0$
4. $p^2=4$

Q. Find the equation of the hyperbola satisfying the give conditions: Foci $(\pm 4,0)$ the latus rectum is of length $12$

Q. Shortest distance (in units) between the two parabolas $y^2=x-2,x^2=y-2$ is

1. $\frac{1}{4\sqrt{2}}$
2. $\frac{5}{4\sqrt{2}}$
3. $\frac{7}{2\sqrt{2}}$
4. $\frac{6}{7\sqrt{2}}$

Q. For hyperbola $-\frac{(x-1{)}^2}{3}+\frac{(y+2{)}^2}{16}=1$ distance between directrices is ?

1. $\frac{32}{\sqrt{19}}$
2. $\frac{2}{\sqrt{19}}$
3. $\frac{3}{\sqrt{19}}$
4. $\frac{4}{\sqrt{19}}$

Q. The equation of the normals at the ends of the latus rectum of the parabola $y^2=4ax$ are given by

1. $x^2-y^2-6ax-6ay+9a^2=0$
2. $x^2-y^2-6ay+9a^2=0$
3. $x^2-y^2-6ax+9a^2=0$
4. $Noneofthese$