If P be a point on the parabola y = 4ax with focus F. Let Q denote the foot of the perpendicular from P onto the directrix. Then, is
1
2
A.
1
Equation of parabola is,
y2 = 4ax ...(i)
Let the parametric coordinate of point P on the parabola is (a, 2a).
Now, ,
PQ = 2a and PF = 2a
we observe that, QF2 = PQ2 + PF2
So, QPF form a right angle isoceles triangle.
In which,
The equations of the circles, which touch both the axes and the line 4x + 3y = 12 and have centres in the first quadrant, are
x2 + y2 + x - y + 1 = 0
x2 + y2 - 2x - 2y + 1 = 0
x2 + y2 - 12x - 12y + 36 = 0
x2 + y2 - 6x - 6y + 36 = 0
If be the roots of the equation x2 - bx + c = 0, Then, which of the following statements is/are correct?
b
Which of the following real valued functions is/are not even functions?
f(x) = x - [x], where [x] denotes the greatest integer less than or equal to x.
In the set of all 3 x 3 real matrices a relation is defined as follows. A matrix A is related to a matrix B, if and only if there is a non-singular 3 x 3 matrix P, such that B = P-1AP. This relation is
reflexive, symmetric but not transitive
reflexive, transitive but not symmetric
symmetric, transitive but not reflexive
an equivalence relation