the point P is the foot of the perpendicular from A(0,t) to the line whose equation is y=tx. Determine

a) the equation of line AP

b) the co-ordinate of P

c) the area of triangle OAP, where O is origin

Question

the point P is the foot of the perpendicular from A(0,t) to the
line whose equation is y=tx Determine
a) the equation of line AP
b) the co-ordinate of P
c) the area of triangle OAP, where O is origin

Gursheen kaur. · Accepted Answer

The given equation is tx-y=0

Coordinates of foot satisfy t(0+Î»t) - (t-Î»)=0 â‡’t(Î»t) - t+Î»=0 $\Rightarrow λ t^{2} - t + λ = 0 \Rightarrow λ (t^{2} + 1) - t = 0 \Rightarrow λ (t^{2} + 1) = t \Rightarrow λ = \frac{t}{(t^{2} + 1)}$ Now, $\Rightarrow F o o t o f p e r p e n d i c u l a r = (\frac{t^{2}}{t^{2} + 1}, t - \frac{t}{t^{2} + 1}) = (\frac{t^{2}}{t^{2} + 1}, \frac{t^{3} + t - t}{t^{2} + 1}) = (\frac{t^{2}}{t^{2} + 1}, \frac{t^{3}}{t^{2} + 1}) = T h e c o o r d i n a t e s o f P$

the point P is the foot of the perpendicular from A(0,t) to the line whose equation is y=tx. Determine a) the equation of line AP b) the co-ordinate of P c) the area of triangle OAP, where O is origin

the point P is the foot of the perpendicular from A(0,t) to the line whose equation is y=tx. Determine

a) the equation of line AP

b) the co-ordinate of P

c) the area of triangle OAP, where O is origin