class 11

Math

Co-ordinate Geometry

Hyperbola

If $2x−y+1=0$ is a tangent to the hyperbola $a_{2}x_{2} −16y_{2} =1$ then which of the following CANNOT be sides of a right angled triangle? (a)$a,4,2$ (b) $a,4,1$(c)$2a,4,1$ (d) $2a,8,1$

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

A hyperbola passes through (2,3) and has asymptotes $3x−4y+5=0$ and $12x+5y−40=0$ . Then, the equation of its transverse axis is $77x−21y−265=0$ $21x−77y+265=0$ $21x−77y−265=0$ $21x+77y−265=0$

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

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

Two tangents to the hyperbola $a_{2}x_{2} −b_{2}y_{2} =1$ having $m_{1}andm_{2}$ cut the axes at four concyclic points. Fid the value of $m_{1}m_{2}˙$

If the base of a triangle and the ratio of tangent of half of base angles are given, then identify the locus of the opposite vertex.

The tangent at a point $P$ on the hyperbola $a_{2}x_{2} −b_{2}y_{2} =1$ meets one of the directrix at $F˙$ If $PF$ subtends an angle $θ$ at the corresponding focus, then $θ=$ $4π $ (b) $2π $ (c) $43π $ (d) $π$

Show that the equation 9$x_{2}−16y_{2}−18x+32y−151=0$ represents a hyperbola. Find the coordinates of the centre, lengths of the axes, eccentricity, latus-rectum, coordinates of foci and vertices, equations of the directrices of the hyperbola.

Find the lengths of the transvers and the conjugate axis, eccentricity, the coordinates of foci, vertices, the lengths of latus racta, and the equations of the directrices of the following hyperbola: $16x_{2}−9y_{2}=−144.$