Conic Section

Q.

Which of the following describes a conic?

Here S is a fixed point and P is the moving point. 'e' is the eccentricity of the conic

1. $\frac{PM}{PS}=e$

2. $\frac{PS}{PM}=e$

3. $\frac{MS}{PS}=e$

4. $\frac{PS}{MS}=e$

Q. The centre of the conic section $2x^2+4y^2+2xy+4x-6y+17=0$ is

1. $(\frac{11}{7},-\frac{8}{7})$
2. $(\frac{11}{7},\frac{8}{7})$
3. $(-\frac{11}{7},\frac{8}{7})$
4. $(-\frac{11}{8},\frac{7}{8})$

Q.

Match the columns by referring to the definition given below.

"A conic is the locus of a point which moves in a plane so that its distance from a fixed point is in a constant ratio to its perpendicular distance from a fixed straight line”.

$\begin{array}{cc}\text{Definition}& \text{Name}\\ \text{P) Fixed point}& \text{1. Axis}\\ \text{Q) Fixed straight line}& \text{2. Vertex}\\ \text{R) Constant ratio}& \text{3. Directrix}\\ \text{S) Line passing through fixed point and perpendicular to fixed line}& \text{4. Focus}\\ & \text{5. Eccentricity}\end{array}$

1. P - 3, Q - 4, R - 5, S - 1

2. P - 4, Q - 3, R - 5, S - 2

3. P - 4, Q - 3, R - 5, S - 1

4. P - 4, Q - 3, R - 1, S - 5

Q. This line $lx+my=n$ is normal to the hyperbola passess through the focus,
then the line can be

1. Transverse axis
2. Latus rectum
3. Conjugate Axis
4. Directrix

Q. The centre of the conic represented by the equation $x^2-6xy+y^2+6x+14y-2=0$ is

1. $(3,2)$
2. $(3,4)$
3. $(-3,4)$
4. $(5,4)$