Maths-
General
Easy
Question
Equation of one of the common tangent of y2 = 4x and 
is equal to-
- x + 2y + 4 = 0
- x + 2y – 4 = 0
- x – 2y – 4 = 0
- None of these
Hint:
find out tangents of curves in slope form and equate the constant terms.
The correct answer is: x + 2y + 4 = 0
x+ 2y+4 =0
Equation of tangent to the parabola in slope form is:
y = mx + 1/m
Equation of tangent to the ellipse in slope form is :
y = mx + √(a2m2+b2)
here, √(a2m2+b2) = 1/m
on squaring both sides, we get
4m2+3 = 1/m2
4m4+3m2-1=0
m2 = -1, ¼
m= ½ or -1/2 when m2= 1/4
equation of tangent :
y=x/2 + 2=> 2y=x+4
y= -x/2 -2 => 2y=-x -4=> x+ 2y+4 =0
a common tangent is a line that is a tangent to more than one curves..
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