Given,
y=x2 ......(i)
x=cost,
y=sint .......(ii)
Which is parametric equation, we change this equation is cartesian equation as follows:
cost=x,sint=y On squaring and adding both i.e.
cost and sin t, we get
x2+y2=cos2t+sin2t ⇒9x2+16y2=25 ........(iii)
[∵cos2θ+sin2θ=1] -The intersection points at Eq. (i) and (iii) are
(1,1) and
(−1,1).
Now, slope of tangent of Eq. (i) at point
(1,1) is
m1==2x ∴ m1=|(1,1)=2 And slope of tangent of Eq. (iii), at point
(1,1) is
m2==− ∴ Angle at point of intersection of Eqs. (i) and (iii), we get
θ1=tan−1|| θ1=tan−1|| =tan−1 Similarly, slope of tangent of Eq. (i) at point
(−1,1) m1=|(−1,1)=−2 And slope of tangent of Eq. (iii) at point
(−1,1) m2== ∴ Angle at point of intersection of Eqs. (i) and (iii), we get
θ2=tan−1|| =tan−1