Distinguishing between Conics from General Equation and Eccentricity

Q. Two parabolas $x^2=4y$ and $y^2=4x$ intersect at two distinct points out of which one of them is origin then the other point will be

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

Q.

The square of distance between the point of intersection of the lines represented by the equation $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ and origin, is

1. 

2. 

3. 

4. None of these

Q. The equation $12x^2-23xy+10y^2-25x+26y-14=0$ represents

1. a parabola
2. a circle
3. a hyperbola
4. an ellipse

Q. The equation $13x^2-18xy+37y^2+2x+14y-2=0$ represents

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

Q. Prove that the lines $y=\sqrt{3}x+1,y=4\mathrm{and}y=-\sqrt{3}x+2$ form an equilateral triangle.

Q. The curve described parametrically by $x=5\cos t$ and $y=2\sin t$ represents

1. Circle
2. Parabola
3. An ellipse
4. Hyperbola

Q. The locus of a point (to the right of $x=2$) whose sum of the distances from the origin and the line $x=2$ is $4$ units, is

1. $y^2=-12(x-3)$
2. $y^2=12(x-3)$
3. $x^2=12(y-3)$
4. $x^2=-12(y-3)$

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

1. Pair of lines
2. Ellipse
3. Parabola
4. Hyperbola

Q. If the equation $k{y}^2+y=x^2-16x+64$ represents a parabola then the value of $|4\Delta |=$

Q. The curve described parametrically by $x=t^2+t,y=2t-1$ represents

1. Circle
2. Parabola
3. An ellipse
4. Hyperbola