An Apache helicopter of enemy is flying along the curve given by `y=x^2+7`. A soldier, placed at (3, 7), wants to shoot down the helicopter when it is nearest to him. Find the nearest distance.

An Apache helicopter of enemy is flying along the curve given by y=x^(2)+7 . A solider, placed at (3, 7), wants to shoot down the helicopter when it is nearest to him. Find the nearest distance.

Find point on y=2x-3 nearest to origin.

Find the equation of tangent to the curve given by x=a sin^(3)t, y=b cos^(3)t at a point where t=(pi)/(2) .

A particle moves along the curve 6y=x^(3)+2 . Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.

If the curve ay+x^(2)=7 and x^(3)=y , cuts orthogonall at (1, 1), then the value of a is ……….

If x = 3, y = 2 is a solution of the equation 5x - 7y = k, find the value of k and write the resultant equation.

A parabolic mirror is silvered at inner surface. The equation of the curve formed by its intersection with X-Y plane is given by y=(x^(2))/(4) . A ray travelling in X-Y plane along line y=x+3 hits the mirror in second quandrant and gets reflected. The unit vector in the direction of reflected ray will be

Find the distance of the line 4x+7y+5=0 from the point (1,2) along the line 2x-y=0 .

A particle moves along the curve y=x^((3)/(2)) in the first quadrant in such a way that its distance from the origin increases at the rate of 11 units/sec. The value of (dx)/(dt) when x = 3 is …………