Conic Sections

A tangent is drawn to the parabola y² = 6x which is perpendicular to the 2x + y = 1. Which of the following points does NOT lie on it?

A hyperbola passes through the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is

If the curve x² + 2y² = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is

Let one focus of the hyperbola $=22$ be at ( $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ ) and the corresponding directrix be $\sqrt[]{10},0$ . If e and $\mathrm{x}=\frac{9}{\sqrt[]{10}}$ respectively are the eccentricity and the length of the latus rectum of H, then $l$ is equal to

Let E₁ : $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$  a > b. Let E₂ be another ellipse such that it touches the end points of major axis of E₁ and the foci of E₂ are the end points of minor axis of E₁. If E₁ and E₂ have same eccentricities, then its value is:             

Let a line L : 2x + y = k, k > 0 be a tangent to the hyperbola $x^2-y^2=3.$  If L is also a tangent to the parabola y² = aX, then a is equal to:

Let r₁ and r₂ be the radii of the largest and smallest circles, respectively, which pass through the point (-4, 1) and having their centres on the circumference of the circle x² + y² + 2x + 4y – 4 = 0. If   $\frac{r_1}{r_2}$ = a + $b\sqrt[]{2},$  then a + b is equal to:

Let P be a variable point on the parabola y = 4x² + 1. Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x is:

Which of the following is equivalent to the Boolean expression $p\wedge \sim q?$

Let B be the centre of the circle $x^2+y^2-2x+4y+1=0.$ Let the tangents at two points P and Q on the circle intersect at the point A(3, 1). Then 8. $\left(\frac{area\Delta APQ}{area\Delta BPQ}\right)$ is equal to ______.