The tangents at the points (at12,2at1) , (at22,2at2) on the parabola y2=4ax are at right angles if_____ t1t2= -2 - Maths - Conic Sections

Question

The tangents at the points (at1
2,2at1) , (at2
2,2at2) on the parabola y2=4ax are
at right angles if_____

t1t2= -2
t1t2= 1
t1t2= 2
t1t2 = -1

Aarushi Mishra · Accepted Answer

Equation of tangent at a point Pt is given byy=xt+atComparing with y=mx+c, slope of tangentm=1tFor point Aat12,2at1 slope of tangentm1=1t1For point Bat22,2at2 slope of tangentm2=1t2If two lines are perpendicular then product of their slope is -1m1m2=-11t1×1t2=-1t1t2=-1

The tangents at the points (at1 2,2at1) , (at2 2,2at2) on the parabola y2=4ax are at right angles if_____ t1t2= -2 t1t2= 1 t1t2= 2 t1t2 = -1

The tangents at the points (at₁ ²,2at₁) , (at₂ ²,2at₂) on the parabola y²=4ax are at right angles if_____

t₁t₂= -2

t₁t₂= 1

t₁t₂= 2

t₁t₂= -1