Eccentricity

Q.

If the distance of the point $(1,–2,3)$ from the plane $x+2y–3z+10=0$ measured parallel to the line, $\frac{x-1}{3}=\frac{2-y}{m}=\frac{z+3}{1}$is $\sqrt{\frac{7}{2}}$ then the value of $\left|m\right|$ is equal to

Q.

The ellipse $x^2+4y^2=4$ is inscribed in a rectangle aligned with the coordinate axes, which is turn in inscribed in another ellipse that passes through the point $\left(4,0\right)$. Then, the equation of the ellipse is

1. $x^2+12y^2=16$

2. $4x^2+48y^2=48$

3. $4x^2+64y^2=48$

4. $x^2+16y^2=16$

Q.

The equation of the ellipse whose foci are at $\left(\pm 2,0\right)$ and eccentricity is $\frac{1}{2}$, is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ Then what is the value of $a^2,b^2$.

1. $a^2=16,b^2=12$

2. $a^2=12,b^2=16$

3. $a^2=16,b^2=4$

4. $a^2=4,b^2=16$

Q.

If a hyperbola passes through the point $P(10,16)$ and it has vertices at $(\pm 6,0)$, then the equation of the normal at $𝑃$ is:

1. $3x+4y=94$

2. $x+2y=42$

3. $2x+5y=100$

4. $x+3y=58$