Home
Class 12
MATHS
If the line lx+my+n=0 touches the hyperb...

If the line `lx+my+n=0` touches the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`. Then

Text Solution

Verified by Experts

The correct Answer is:
`a^(2)l^(2)-b^(2)m^(2)=n^(2)`
Promotional Banner

Topper's Solved these Questions

  • THE HYPERBOLA

    ML KHANNA|Exercise PROBLEM SET (3) (MCQ)|8 Videos

  • THE HYPERBOLA

    ML KHANNA|Exercise PROBLEM SET (3) (TRUE AND FALSE) |5 Videos

  • THE HYPERBOLA

    ML KHANNA|Exercise PROBLEM SET (2) (TRUE AND FALSE)|2 Videos

  • THE ELLIPSE

    ML KHANNA|Exercise SELF ASSESSMENT TEST|9 Videos

  • THE PARABOLA

    ML KHANNA|Exercise MISCELLANEOUS EXERCISE (Assertion/ Reason)|1 Videos

Similar Questions

Explore conceptually related problems

If the line lx+my +n=0 touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then

The pole of the line lx+my+n=0 with respect to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , is

The line 2x+y=1 is tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1. If this line passes through the point of intersection of the nearest directrix and the x-axis,then the eccentricity of the hyperbola is

If the line lx+my=1 is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then (a^(2))/(l^(2))+(b^(2))/(m^(2))=

If the straight line 2x+sqrt(2)y+n=0 touches the hyperbola (x^(2))/(9)-(y^(2))/(16)=1, then find the value of n.

If the line lx+my+n=0 cuts the ellipse ((x^(2))/(a^(2)))+((y^(2))/(b^(2)))=1 at points whose eccentric angles differ by (pi)/(2), then find the value of (a^(2)l^(2)+b^(2)m^(2))/(n^(2))

The line lx+my=n is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, if

The line lx+my+n=0 is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1. then prove that (a^(2))/(l^(2))+(b^(2))/(m^(2))=((a^(2)-b^(2))^(2))/(n^(2))