Solve this: Two parabola have the focus (3, -2) Their directions are the x-axis, and the y-axis respectively - Maths - Conic Sections

Question

Solve this:
Two parabola have the focus (3, -2) Their directions are the
x-axis, and the y-axis respectively Then the slope of their common
chord is:
( A )   - 1              
                 
                 
                 
    ( B )   - 1 2 ( C )   - 3 2    
                 
                 
                  ( D
)   1 2

Ankita Agarwal · Accepted Answer

Dear Student,

The equation of a parabola with focus (a, b) and directrix lx+my+n=0 is (x-a)2 +(y-b)2=(lx+my+n)2 l2+m2Given parabolas have the same focus (-3, 2)
 The directrix of one parabola is y=0 and that of the other is x=0
   Thus, equation of first parabola is  (x+3)2 +(y-2)2=x212  =x2+9+6x+y2+4-4y=x2=y2 +6x-4y+13=0   Similarly, the equation of the second parabola is,     (x+3)2 +(y-2)2 = y212=x2+9+6x+y2+4-4y=y2=x2+6x-4y+13=0Subtracting the second equation from the first equation, we gety2 +6x-4y+13-x2+6x-4y+13 = 0y2 +6x-4y+13-x2-6x+4y-13= 0y2 -x2=0  (y-x)(y+x)=0   The above equation represents a pair of intersecting lines  y-x=0 and y+x=0  i
e
, y=x and y=-x   Here, the line y=x is not a common chord as it does not even touch the second parabola
   So, the only common chord is the line  y=-x  i
e
, y=(-1)x  On Compairing with y = mx+c m= -1, which is the slope
So, the slope of the common chord is -1

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Solve this: Two parabola have the focus (3, -2). Their directions are the x-axis, and the y-axis respectively. Then the slope of their common chord is: ( A ) - 1 ( B ) - 1 2 ( C ) - 3 2 ( D ) 1 2

Solve this:
Two parabola have the focus (3, -2). Their directions are the x-axis, and the y-axis respectively. Then the slope of their common chord is:
$(A) - 1 (B) - \frac{1}{2} (C) - \frac{\sqrt{3}}{2} (D) \frac{1}{2}$