General Equation of Conics

Q. The conic represented by the equation $x^2+y^2+2xy+4x-6y+17=0$ is

Q.

Find the image of P(-3, 5) about the line x - y + 2 = 0

1. (2, 0)

2. (1, 3)

3. (3, -1)

4. (0, 2)

Q. If the curve passing through $P(4,2),$ satisfying the differential equation $\frac{dy}{dx}=\frac{y}{x-y^2}$ is a conic, then which of the following statements is (are) correct?

1. Focus of the conic lies on line $y=2$.
2. Equation of directrix of conic is $4x–17=0$.
3. Eccentricity of the conic is $1$.
4. Eccentricity of the conic is $3$.

Q. The equation $25(x^2+y^2-2x+1)=(4x-3y+1{)}^2$ represents

1. an ellipse
2. a parabola
3. a hyperbola
4. a pair of straight lines

Q.

Match the column

$\begin{array}{cc}\text{Equation}& \text{Name of the curve}\\ \text{1)}{x}^2-2x-y-3=0& \text{P) Circle}\\ \text{2)}{x}^2+3xy+2y^2-x-4y-6=0& \text{Q) Parabola}\\ \text{3)}{x}^2+y^2-20=0& \text{R) Ellipse}\\ \text{4)}7x^2+7y^2+2xy+10x-10y+7=0& \text{S) Hyperbola}\\ \text{5)}6x^2-xy-y^2-23x+4y+15=0& \text{T) Pair of straight lines}\end{array}$

1. $1-T,2-Q,3-P,4-R,5-S$

2. $1-Q,2-T,3-P,4-R,5-S$

3. $1-Q,2-T,3-P,4-S,5-R$

4. $1-Q,2-S,3-P,4-T,5-R$