Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
1.3k views
in Differential equations by (54.8k points)

Consider a family of curves, where the ordinate is proportional to the cube of the abscissa and let A be a fixed point, which has coordinates (a, b).

If the tangent through A to a curve cuts the curve again at a point B, then the locus of B is 

(A) xy - 4bx + 3ay = 0 

(B) 2xy + bx - 3ay = 0 

(C) x2 - 3y2 = ax - 3by 

(D) a2x2 + b2y2 = 1 

1 Answer

+1 vote
by (52.5k points)
selected by
 
Best answer

Answer is (A) xy - 4bx + 3ay = 0

Let point of contact of tangent P is (αλα3) through point A(αβ) and let this tangent cuts the curve again at point B (βλβ3).

Slope of PB = Slope of tangent at point P

Slope of PA = Slope of tangent at point P

Hence, locus of B is xy - 4bx + 3ay = 0.

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.

...