Question

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

Solution

Correct option is

(2, 3)

Any point on the ellipse is given by 

                                       

Hence the equation of the tangent at  is

                 

Therefore, the tangent cuts the coordinate axes at the points

                            

Thus the area of the triangle formed by this tangent and the coordinate axes is

                                

                                           

But cosec 2θ is smallest when θ = π/4. Therefore A is smallest when θ = π/4.

Hence the required points is

                    

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

 

Q6

If ab > 0 then the minimum value of  

Q7

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

Q8

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

Q9

The tangent to the curve 

At the point corresponding to  is

Q10

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