Solve this: Q112 Two common tangents to the circle x2 + y2 = 2a2 and parabola y2 = - Maths - Relations and Functions

Question

Solve this:

Q112 Two common tangents to the circle x2 +
y2 = 2a2 and parabola y2 = 8ax
are

(a) x = ± (y +2a ) (b) y = ± (x + 2a)

(c) x = ± (y + a) (d) y = ± (x + a)

Shruti Tyagi · Accepted Answer

Dear student,

Equation of tangent to the parabola in slope form: y=mx+2am                   
(1)The Equation of any tangent to the parabola y2=8ax will touch the circle x2+y2=2a2 or, Eqn of circle can be written as  x2+y2=2a2if radius=2a=length of  the perpendicular from the centre(0,0) to the lineor, 2a=2am1+m2Squaring both sides⇒2a2= 4a2m21+m2⇒2a21+m2=4a2m2⇒m21+m2=2⇒m2+m4-2=0⇒m4+m2-2=0⇒m4+2m2-m2-2=0⇒m2m2+2-1m2+2=0⇒m2+2m2-1=0But m2+2=0 gives non real values of m
 and m2-1=0⇒m2=1⇒m=±1put m=±1 in (1) y=±1×x+2a±1⇒y=x+2a and y=-x-2a⇒y=x+2a and y=-x+2aor y=±x+2aThus option b is correct
Regards

Solve this: Q112. Two common tangents to the circle x2 + y2 = 2a2 and parabola y2 = 8ax are (a) x = ± (y +2a ) (b) y = ± (x + 2a) (c) x = ± (y + a) (d) y = ± (x + a)

Solve this:

Q112. Two common tangents to the circle x² + y² = 2a² and parabola y² = 8ax are

(a) x = $\pm$ (y +2a ) (b) y = $\pm$ (x + 2a)

(c) x = $\pm$ (y + a) (d) y = $\pm$ (x + a)