A triangle is inscribed in the hyperbola...

A triangle is inscribed in the hyperbola `xy=c^2` and two of its sides are parallel to `y=m_1 x and y = m_2 x`. Prove that the third side touches the hyperbola `4m_1 m_2 xy = c^2 (m_1 + m_2)^2`.

Similar Questions

Explore conceptually related problems

If y+b=m_1(x+a) and y+b=m_2(x+a) are two tangents to the paraabola y^2=4ax then

If a normal of slope m to the parabola y^2 = 4 a x touches the hyperbola x^2 - y^2 = a^2 , then

The area of the triangle whose sides y=m_1 x + c_1 , y = m_2 x + c_2 and x=0 is

Two straight lines (y-b)=m_1(x+a) and (y-b)=m_2(x+a) are the tangents of y^2=4a xdot Prove m_1m_2=-1.

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+c)=0 , then m_1+m_2=0 (b) 1+m_1+m_2=0 m_1m_2-1=0 (d) 1+m_1m_2=0

Find the value of m for which y = mx + 6 is a tangent to the hyperbola x^2 /100 - y^2 /49 = 1

Show that an infinite number of triangles can be inscribed in the rectangular hyperbola xy-c^2 = 0 whose all sides touche the parabola y^2 = 4ax .

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+a)=0 , then (a) m_1+m_2=0 (b) 1+m_1+m_2=0 (c) m_1m_2-1=0 (d) 1+m_1m_2=0

The locus of the mid - points of the parallel chords with slope m of the rectangular hyperbola xy=c^(2) is