Two straight lines are perpendicular to each other.One of them touches the parabola y2=4a(x+a) and the other touches y2=4b(x+b) .The locus of the point of intersection of the two lines is
A
x + a = 0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
x + b = 0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x + a + b = 0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
x – a – b = 0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is C x + a + b = 0 Equation of tangent to the parabola y2=4a(x+a)isy=m(x+a)+am..........(1)
Equation of tangent to the parabola y2=4b(x+b)isy=m1(x+b)+bm1..........(2)
Since the tangents are perpendicular mm1=−1⇒m1=−1m ∴ (2) can be written as y=(−1m)(x+b)−bm.......(3) (1)−(3)⇒0=x(m+1m)+a(1+1m)+b(m+1m)⇒x+a+b=0
Equation of the locus is x +a+b = 0