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
If 2x + y + k = 0 is a normal to the parabola y2 = - 8x, then the value of k, is
8
16
24
32
C.
24
The equation of any normal to the parabola
y2 = - 8x is y = mx + 4m + 2m3 ... (i)
[ using equation of normal of parabola in slope form y = mx - 2am - am3 and a = - 2]
But, the given normal is
2x + y + k = 0
y = - 2x - k ...(ii)
Comparing Eqs. (i) and (ii), we get
m = - 2
and - 4m - 2m3 = k
k = 8 + 16 = 24
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
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