The graph of the function y = f(x) is symmetrical about the line x = 2, then
f(x + 2)= f(x – 2)
f(2 + x) = f(2 – x)
f(x) = f(-x)
f(x) = f(-x)
If 2a + 3b + 6c =0, then at least one root of the equation ax2 + bx+ c = 0 lies in the interval
(0,1)
(1,2)
(2,3)
(2,3)
If the sum of the slopes of the lines given by x2 -2cxy -7y2 =0 is four times their product, then c has the value
-1
2
-2
-2
The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is –1 is
If one of the lines given by 6x2 -xy +4cy2 = 0 is 3x + 4y = 0, then c equals
1
-1
3
3
D.
3
The pair of lines is 6x2-xy +4cy2 =0
On comparing with ax2 +2hxy by2 = 0
we get a = 6, 2h =-1, b= c
therefore
m1 +m2 = -2h/b = 1/4c and m1m2 = a/b = 6/4c
On line of given pair of lines is
3x+4y = 0
slope of line = -3/4 = m1
-3/4 +m2 = 1/4c
m2 = 1/4c + 3/4
1 + 3c = -8 3c = -9
⇒ c = -3
If a circle passes through the point (a, b) and cuts the circle x2 +y2= 4 orthogonally, then the locus of its centre is
2ax +2by + (a2 +b2+4)=0
2ax +2by - (a2 +b2+4)=0
2ax -2by - (a2 +b2+4)=0
2ax -2by - (a2 +b2+4)=0
A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is
(x-p)2 = 4qy
(x-q)2 = 4py
(y-p)2 = 4qx
(y-p)2 = 4qx
If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference 10π, then the equation of the circle is
x2 + y2- 2x +2y -23 = 0
x2 - y2- 2x -2y -23 = 0
x2 - y2- 2x -2y +23 = 0
x2 - y2- 2x -2y +23 = 0