K. C. Sinha Solutions for Chapter: Conic Section, Exercise 1: 7.1

Which of the following statements are true?

Which of the following statements are true?

If $m$ be the slope of common tangent to the circle $x^2+y^2=16$ and ellipse $\frac{x^2}{25}+\frac{y^2}{4}=1$ in the first quadrant, then $81{ m}^8=$

Points $A,B$ and $C$ lie on the parabola $y^2=4ax$. The tangents to the parabola at $A,B$ and $C$ taken in pairs, intersect at points $P,Q$ and $R$. If area of $∆ABC$ is $16$ square units, then area of $∆PQR$ is 

Tangents $PT$ and $QT$ to the parabola $y^2=4x$ intersect at $T$ and the normals drawn at the points $P$ and $Q$ intersect at the point $R\left(9,6\right)$ on the parabola. If $O$ be the origin then $O{T}^6=$

An ellipse having semi major and minor axes $24$ units and $7$ units slides between two lines at right angles to one another. If $A$ be the area enclosed by the locus of the centre of the ellipse, then $\frac{10}{\pi }A=$

The eccentric angles of the vertices of a triangle inscribed in the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ are $\alpha ,\beta ,\gamma$, then for the area of this triangle to be greatest, the angle subtended by the two consecutive vertices of the triangle at the centre of the ellipse in degree measure is

The locus of the point of intersection of the tangents to $y^2=4x+4$ and $y^2=8x+16$ which are perpendicular to each other is $x=-k$. Then $k=$