What is Eccentricity in Conic Sections?

Let $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,a>0,b>0,$ be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $4\left(2\sqrt[]{2}+\sqrt[]{14}\right).$ If the eccentricity H is $\frac{\sqrt[]{11}}{2},$ then the value of a² + b² is equal to………….

Let the tangent to the circle C₁ : x² + y² = 2 at the point M(1, 1) intersect the circle $C_2:{\left(x-3\right)}^2$ + ${\left(y-2\right)}^2=5,$ at two distinct points A and B. If the tangents to C₂ at the points A and B intersect at N, then the area of the triangle ANB is equal to:

Let PQ be a focal chord of the parabola y2 = 4x such that it subtends an angle of $\frac{\pi }{2}$ at the point (3, 0). Let the line segment PQ be also a focal chord of the ellipse E: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$ $a^2>b^2.$ If e is the eccentricity of the ellipse E, then the value of $\frac{1}{e^2}$ is equal to:

If the line x – 1 = 0 is a directrix of the hyperbola kx² – y² = 6, then the hyperbola passes through the point

Let the abscissae of two points P and Q on a circle be the roots of x² – 4x – 6 = 0 and the ordinates of P and Q be the roots of y² + 2y – 7 = 0. If PQ is a diameter of the circle x² + y² + 2ax + 2by + c = 0, then the value of (a + b +) is……………