Home
Class 12
MATHS
Let P(a sectheta, btantheta) and Q(asec...

Let `P(a sectheta, btantheta) and Q(asecphi , btanphi)` (where `theta+phi=pi/2`) be two points on the hyperbola `x^2/a^2-y^2/b^2=1` If `(h, k)` is the point of intersection of the normals at `P and Q` then `k` is equal to
(A) `(a^2+b^2)/a` (B) `-((a^2+b^2)/a)` (C) `(a^2+b^2)/b` (D) `-((a^2+b^2)/b)`

Text Solution

Verified by Experts

The correct Answer is:
`k=- ((a^(2)+b^(2))/(b))`
Promotional Banner

Similar Questions

Explore conceptually related problems

if P(theta) and Q(pi/2 +theta) are two points on the ellipse x^2/a^2+y^@/b^2=1 , locus ofmid point of PQ is

If P(theta),Q(theta+pi/2) are two points on the ellipse x^2/a^2+y^2/b^2=1 and α is the angle between normals at P and Q, then

Let P(6,3) be a point on the hyperbola x^2/a^2-y^2/b^2=1 If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is

If (asectheta;btantheta) and (asecphi; btanphi) are the ends of the focal chord of x^2/a^2-y^2/b^2=1 then prove that tan(x/a)tan(phi/2)=(1-e)/(1+e)

Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1 If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is

If (asectheta, btantheta) and (asecphi, btanphi) be two coordinate of the ends of a focal chord passing through (ae,0) of x^2/a^2-y^2/b^2=1 then tan(theta/2)tan(phi/2) equals to

If P(a sec alpha,b tan alpha) and Q(a secbeta, b tan beta) are two points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 such that alpha-beta=2theta (a constant), then PQ touches the hyperbola

If two points P & Q on the hyperbola , x^2/a^2-y^2/b^2=1 whose centre is C be such that CP is perpendicularal to CQ and a lt b 1 ,then prove that 1/(CP^2)+1/(CQ^2)=1/a^2-1/b^2 .

If two points P & Q on the hyperbola , x^2/a^2-y^2/b^2=1 whose centre is C be such that CP is perpendicularal to CQ and a lt b 1 ,then prove that 1/(CP^2)+1/(CQ^2)=1/a^2-1/b^2 .

If the normal at P(asectheta,btantheta) to the hyperbola x^2/a^2-y^2/b^2=1 meets the transverse axis in G then minimum length of PG is