The Coordinates Of The Point P on The Curve y2 = 2x3, The Tangent At Which Is Perpendicular To The Line 4x – 3y + 2 = 0, Are Given By

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.



The coordinates of the point P on the curve y2 = 2x3, the tangent at which is perpendicular to the line 4x – 3y + 2 = 0, are given by


Correct option is

(1/8, 1/16)

Differentiating y2 = 2x3, we get


The slope of the line 4x – 3y + 2 = 0 is 4/3. Therefore, the coordinates of P(xy) must satisfy


Also, y2 = 2x3. Solving these, we get x = 1/8 and y = –1/16

 (clearly x ≠ 0).



A dynamite blast blows a heavy rock starting up with a launch velocity to 160 m/sec. It reaches a height of s = 160t – 16t2 after t sec. The velocity of the rock when it is 256 m above ground on the way up is


The slope of the tangent to the curve represented by x = t2 + 3t – 8 and y = 2t2 – 2t – 5 at the point M (2, 1) is


The coordinates of points P(xy) lying in the first quadrant on the ellipsex2/8 + y2/18 = 1 so that the area of the triangle formed by the tangent at Pand the coordinate axes is the smallest, are given by


The points(s) on the curve y3 + 3x2 = 12y where the tangent is vertical is(are)


The equation of the common tangent to the curves y2 = 8x and xy = –1 is 



If ab > 0 then the minimum value of  


The curve y = ax3 + bx2 + cx + 8 touches x – axis at P(2, 0) and cuts they – axis at a point Q where its gradient is 3. The value of a, b, c are respectively


If the tangent at (1, 1) on y2 = x(2 – x)2 meets the curve again at P, is


The tangent to the curve 

At the point corresponding to  is


The points of contact of the vertical tangents to x = 2 – 3 sinθ,  y = 3 + 2 cos θ are