about to only mathematics

Options

A. y=0, y=4(x-1)
B. y=0, y=-4(x-1)
C. y=0, y=-30x-50
D. none of these

Answer

A

Explanation

The equations of tangent to `y=x^(2)` is
`x=my+1/(4m)" ...(1)"`
The equation of tangent to y `y=-(x-2)^(2)`is
`x=my+1/(4m)" ...(1)"`
Lines gives in (i) and (ii) represent the same line.
`:." "1/(4m)=2-1/(4m)rArr=1/4`
Substituting m=1/4 in (i), we get y=4(x-1) as a common tangent.
Clearly, `y=x^(2)" and "y=-(x-2)^(2)` represent parabolas having vertex at (0, 0) and (2, 0) respectively and touching x-axis i.e. y=0 is also a common tangent.