A rod of length l slides with its ends on two perpendicular lines. Then, the locus of its mid point is
None of these
The equation of straight line through the intersection of line 2x +y = 1 and 3x + 2y = 5 and passing through the origin is
7x + 3y = 0
7x - y = 0
3x + 2y = 0
x + y = 0
The line joining (5, 0) to () is divided internally in the ratio 2 : 3 at P. If 0 varies, then the locus of P is
a straight line
a pair of straight lines
a circle
None of the above
The condition that the line lx + my = 1 may be normal to the curve y2 = 4ax, is
al3 - 2alm2 = m2
al2 + 2alm3 = m2
al3 + 2alm2 = m3
al3 + 2alm2 = m2
D.
al3 + 2alm2 = m2
We know that the equation of normal to the curve y2 = 4ax in slope form is
y = Mx - 2aM - aM3 ...(i)
Also, given equation of normal to y2 = 4ax, is
y = ...(ii)
On comparing Eqs. (i) and (ii), we get
If the equation of an ellipse is 3x2 + 2y2 + 6x - 8y + 5 = 0, then which of the following are true?
e =
centre is (- 1, 2)
foci are (- 1, 1) are (- 1, 3)
All of the above