the locus of the mid point of the portion of the tangent to the ellipse( x^2/a^2)+(y^2/b^2)=1 included between the coordinate - Maths - Conic Sections

Question

the locus of the mid point of the portion of the tangent to the
ellipse( x^2/a^2)+(y^2/b^2)=1 included between the coordinate axis
is

Rahul Raj · Accepted Answer

Dear student

parametric equation of tangent to ellipsex2a2+y2b2=1isxcosθa+ysinθb=1it touches the coordinate axes at (asecθ,0) and (0,bcosecθ)let the midpoint of portion of tangent be (h,k)so, (h,k)=(asecθ/2,bcosecθ/2) which is midpoint of (asecθ,0) and (0,bcosecθ)h=asecθ/2 gives cosθ=a/2hk=bcosecθ/2 gives sinθ=b/2kcos2θ+sin2θ=1a2h2+b2k2=1or a2k2+b2h2=4h2k2so locus is a2y2+b2x2=4x2y2

Regards

the locus of the mid point of the portion of the tangent to the ellipse( x^2/a^2)+(y^2/b^2)=1 included between the coordinate axis is