Class 11

Math

Co-ordinate Geometry

Hyperbola

Tangents are drawn to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ at two points whose eccentric angles are $α−β$ and $α+β$ The coordinates of their point of intersection are

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Two straight lines pass through the fixed points $(±a,0)$ and have slopes whose products is $p>0$ Show that the locus of the points of intersection of the lines is a hyperbola.

If the tangents to the parabola $y_{2}=4ax$ intersect the hyperbola $a_{2}x_{2} −b_{2}y_{2} =1$ at $AandB$ , then find the locus of the point of intersection of the tangents at $AandB˙$

Find the eccentricity of the hyperbola given by equations $x=2e_{t}+e_{−1} andy=3e_{t}−e_{−1} ,t∈R˙$

The lines parallel to the normal to the curve $xy=1$ is/are $3x+4y+5=0$ (b) $3x−4y+5=0$ $4x+3y+5=0$ (d) $3y−4x+5=0$

Find the equation of the common tangent to the curves $y_{2}=8x$ and xy=-1.

(x-1)(y-2)=5 and $(x−1)_{2}+(y+2)_{2}=r_{2}$ intersect at four points A, B, C, D and if centroid of $△ABC$ lies on line $y=3x−4$ , then locus of D is

Find the equation of hyperbola : Whose center is (1,0), focus is (6,0) and the transverse axis is 6

Find the vertices of the hyperbola $9x_{2}−16y_{2}−36x+96y−252=0$