Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
If two tangents to the parabola y2=4ax form a point P make angles θ1 and theta 2 with the axis of parabola then find the locus of point P such that theta1+theta2=pi/2
Dear vanya saxena tangent at parabola at (at12,2at1) is yt1 =x+at12 so tangebt at (at22,2at2) is yt2 =x+at22 these tangent meat at point P so point p is {at1t2,a(t1 +t2)} also tan Θ1 =1/t1 tanΘ 2 =1/t2 and tan(Θ1 + Θ2) = tan pi/2 simplify so t1t2 =1 locus of point p x=at1t2 x=a Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Askiitians Experts Badiuddin
Dear vanya saxena
tangent at parabola at (at12,2at1) is yt1 =x+at12
so tangebt at (at22,2at2) is yt2 =x+at22
these tangent meat at point P
so point p is
{at1t2,a(t1 +t2)}
also tan Θ1 =1/t1
tanΘ 2 =1/t2
and tan(Θ1 + Θ2) = tan pi/2
simplify
so t1t2 =1
locus of point p
x=at1t2
x=a
Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Askiitians Experts Badiuddin
as in the given question the two tangents are perpendicular and the locus of perpendicular tangents is director circle and in case of parabola director circle is directrix and in the question directrix is x=a which is is required locus
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -