Equation of Tangent When a Point Is Given

Q. A tangent is drawn at a point on the parabola $y^2=10x$. If this tangent intersect the parabola $y^2=10x+p$ at 2 points; then,

1. $-10<p<10$
2. $p<0$
3. $p>0$
4. p = 0

Q. Let $t_{1}and{t}_2$ be the parameters of 2 points on a parabola. What is the value of $t_1{t}_2$ if tangents at these points are at right angle to each other?
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Q.

A tangent is drawn at the point $P(\alpha ,\beta )$ on the parabola $y^2=4ax$. This tangent meets a second parabola $y^2=4a(x+k)$ at A and B, what is the midpoint of AB?

1. 

2. 

3. 

4. 

Q. A tangent is drawn at a point on the parabola $y^2=10x$. If this tangent intersect the parabola $y^2=10x+p$ at 2 points; then,

1. -10 < p < 10

2. p < 0

3. p > 0

4. p = 0

Q.

P(t = 2) is a point on the parabola $y^2=4ax$. What is the point of the intersection of tangent at P and the directrix of the parabola?

1. (-10, 15)

2. (15, 10)

3. (0, 0)

4. (10, 10)

Q.

A tangent is drawn at the point $P(\alpha ,\beta )$ on the parabola $y^2=4ax$. This tangent meets a second parabola $y^2=4a(x+k)$ at A and B, what is the midpoint of AB?

1. $(\alpha +k,\beta )$

2. $(\alpha -k,\beta -k)$

3. $[\frac{\alpha }{k},\frac{\beta }{k}]$

4. $(\alpha ,\beta )$

Q. If tangent to the parabola $y^2=4x$ is also normal to $x^2=4by$ and $|b|\le \frac{1}{\sqrt{k}}$, then the numerical value of $k$ is

Q. Let $t_{1}and{t}_2$ be the parameters of 2 points on a parabola. What is the value of $t_1{t}_2$ if tangents at these points are at right angle to each other?
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