5) Through the vertex O of the parabola y2 = 4ax a perpendicular is drawn to any tangent meeting it - Maths -

Question

5) Through the vertex O of the parabola y2 = 4ax
a perpendicular is drawn to any tangent meeting it at P and the
parabola at Q Then OP OQ = ___
1) a2 2) 2a2 3) 3a2 4)
4a2

Shivam Mishra · Accepted Answer

Dear Student,

The language of question is not clear
I assume that O is vertex , P is point where perpendicular meets tangent
Equation of tangent y2=4ax at at2,2atyt=x+at2⇒x-yt+at2=0
iLength of perpendicular from O0,0 is OP=0+0+at21+t2⇒OP=at21+t2Equation of perpendicular to i is tx+y=kIt passes through 0,00+0=ktx+y=0y=-tx put in y2=4axt2x2=4ax⇒x=4at2y=-tx=-t 4at2=-4atHence Q4at2,-4atBy distance formulaOQ=4at2-02+-4at-02=4a1t4+1t2=4a1+t2t4OQ=4at21+t2OP
OQ=at21+t2 4at21+t2=4a2 Answer

5) Through the vertex O of the parabola y2 = 4ax a perpendicular is drawn to any tangent meeting it at P and the parabola at Q. Then OP.OQ = ___ 1) a2 2) 2a2 3) 3a2 4) 4a2

5) Through the vertex O of the parabola y² = 4ax a perpendicular is drawn to any tangent meeting it at P and the parabola at Q. Then OP.OQ = ___
1) a² 2) 2a² 3) 3a² 4) 4a²