The length of the subnormal to the parabola y2 = 4dx at any point is equal to:
√2 a
2√2 a
a/√2
2a
The normal at the point ( 1, 1 ) to the curve 2y =3 -x2 is:
x + y = 0
x + y + 1 = 0
x - y + 1 = 0
The coordinates of the point of the curve y = x2 + 3x + 4 the tangent at which passes through the origin are:
( 2, 14 ), ( -2, 2 )
( 2, 14 ), ( -2, -2 )
( 2, 14 ), ( 2, 2 )
None of these
If the rate of change of area of a circle is equal to the rate of change of its diameter,then its radius =
Tangents to curve y = x3 at x = -1 and x = 1 are
Parallel
Intersecting obliquely
Perpendicular to each other
The equation of the tangent to the curve y = 2 x2 - 3x - 1 at the point (1,-2) is
x - y - 3 = 0
x - y + 3 = 0
x + y - 3 = 0
x + y + 3 = 0
Two towns A and B are 60 km a part A school is to be built to serve 150 students.If the total distance to be traveled by all 200 students is to be as small as possible, then the school should be built at
Town B
Town A
45 km from town B
The equation of the normal of the curve y = x (2 - x ) at the point ( 2, 0 ) is
x - 2y = 2
2x + y = 4
x - 2y + 2 = 0
The side of an equilateral triangle is 2 cm and is increasing at the rate of 8 cm/hr.The area of the triangle is increasing at the rate of
8√3 sq.cm/hr
4√3 sq.cm/hr
√3/8 sq cm/hr
