HyperbolaMedium

Question

The tangent to the hyperbola xy = c2 at the point P intersects the x-axis at T and the y-axis ′T′. The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N′. The areas of the triangles PNT and PN ′T′ are ᐃ and ᐃ′  respectively, then is -

Options

A.equal to 1
B.depends on t
C.depends on c
D.equal to 2

Solution

       
Let point P be
Equation of tangent at P is
x + yt2 = 2ct
∴  T is (2ct, 0) & T′ is
Now equation of normal at P is
t2 x - y = ct3 - c/t
∴ N
ᐃ = =
ᐃ′ = c2 (1 + t4)
∴ .

Create a free account to view solution

View Solution Free
Topic: Hyperbola·Practice all Hyperbola questions

More Hyperbola Questions

The normal at one extremity of latus rectum (in 1st quadrant) of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} ...The equation to the chord joining two points $\left( x_{1},y_{1} \right)$ and $\left( x_{2},y_{2} \right)$ on the rectan...Variable circles are drawn touching two fixed circles externally, then locus of centre of variable circle is -...Solutions of the differential equation $\left( 1 - x^{2} \right)\frac{dy}{dx} + xy = ax$ where $a \in R$, is:...If 2x - y + 1 = 0 is a tangent to the hyperbola x2a2-y216=1, then which of the following CANNOT be sides of a right angl...