Sarthaks Test
+1 vote
145 views
in Mathematics by (145 points)
closed by

36. The equation of common tangent to y2 = 4ax and x2=4ay is
37. Parabola P always passes through the points

2 Answers

+2 votes
by (273 points)
selected by
 
Best answer

36.

The equation of any tangent to y2=4ax is

y=mx+ma​

If it touches x2=4ay then, the equation.

⇒x2=4a(mx+ma​) has equal roots.

⇒mx2−4am2x−4a2=0 has equal roots

If the roots are equal, the discriminant is equal to 0

i.e.,b2−4ac=0

⇒16a2m4+16a2m=0

⇒16a2m4=−16a2m

m=−1

Putting m=−1 in y=mx+am we get,

y=−x−a

⇒x+y+a=0 This is the common tangent to the two parabola.

+1 vote
by (273 points)
37. option D (-a, 0), (0, a)

Related questions

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...