The Condition That The Line  be A Normal To The Parabola   Y2 = 4ax is

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Question

The condition that the line  be a normal to the parabola  

y2 = 4ax is

Solution

Correct option is

p3 = 2ap2 + aq2

….. (1) is normal of y2 = 4ax. Its slope is . But equation of normal of parabola y2 = 4axis

y = mx – 2am – am3.

Comparing this with (1). q = – 2am – am3.

  

 p3 = 2ap2 + aq2.

 

SIMILAR QUESTIONS

Q1

If the straight line x + y = 1 touches the parabola y2 – y + x = 0, then the coordinates of the point of contact are

Q2

The angle of intersection between the curves y2 = 4x and x2 = 32y at point (16, 8) is

Q3

The pole of the line lx + mx + n = 0 with respect to the parabola y2 = 4ax is

Q4

Two tangent are drawn from the point (–2, –1) to the parabola y2 = 4x. if  is the angle between them, then 

Q5

The conic represented by the equation  is

Q6

If (4, 0) is the vertex and y-axis, the directrix of a parabola then its focus is

Q7

The straight line y = mx + c touches the parabola y2 = 4a(x + a) if

Q8

The focus of the parabola x2 – 2x – y + 2 = 0 is

Q9

If P1Q1 and P2Q2 are two focal chords of the parabola y2 = 4ax, then the chords P1P2 and Q1Q2 intersect on the

Q10

The equation of the normal to the hyperbola y2 = 4x, which passes through the point (3, 0), is