M L Aggarwal Solutions for Chapter: Conic Sections, Exercise 10: CHAPTER TEST

Show that the equation $5x^2+30x+2y+15=0$ represents a parabola. find its vertex, focus, length of latus rectum and equations of directrix and axis of parabola?

Find the equation of the parabola with its axis parallel to $y$-axis and passing through the points $\left(4,5\right),\left(-2,11\right) \mathrm{and} \left(-4,21\right)$.

Identify the curve represented by $2x^2-10xy+12y^2+10x-16y-3=0$?

Identify the curve represented by $9x^2-24xy+16y^2-6x+8y-5=0$?

Identify the curve represented by $6x^2-5xy-6y^2+14x+6y-4=0$?

Show that the line $y=x+\sqrt{\frac{5}{6}}$ touches the ellipse $3x^2+2y^2=1$. Also find the coordinates of the point of contact?

Determine $k$ so that the line $2x+y+k=0$ may touch the hyperbola $3x^2-y^2=3$?

Find the equations of tangents to the ellipse $4x^2+5y^2=20$ which are perpendicular to the line $3x+2y-5=0$.