Home
Class 12
MATHS
Find the equation of the straight lines ...

Find the equation of the straight lines touching both `x^2+y^2=2a^2` and `y^2=8a xdot`

Text Solution

Verified by Experts

The correct Answer is:
`xpmy+2a=0`

The equation of tangent to the parabola `y^(2)=8ax` having slope m is
`y=mx+(2a)/(m)` (1)
the equation of tangent to the circle `x^(2)+y^(2)=2a^(2)` having slope m is
`y=mxpmsqrt(2a)sqrt(1+m^(2))` (2)
Equation (1) and (2) are identical. Therefore,
`(2a)/(m)=pmsqrt(2)asqrt(1+m^(2))`
`orm^(4)+m^(2)-2=0`
`or(m^(2)+2)(m^(2)-1)=0`
`orm^(2)-1=0`
`orm=pm1`
Hence, the required tangents are `x+y+2a=0`.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE ENGLISH|Exercise Concept Applications Exercise 5.5|9 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise Concept Applications Exercise 5.6|8 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise Concept Applications Exercise 5.3|7 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE ENGLISH|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE ENGLISH|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

Find the differential equation of all straight lines touching the circle x^2+y^2=a^2

Find the equation of the family of circles touching the lines x^2-y^2+2y-1=0.

The equation to the line touching both the parabolas y^2 =4x and x^2=-32y is

Find the equation of the straight line passing through the point (2, -6) and the point of intersection of the lines 5x-2y+14=0 and 2y=8-7x .

Find the equation of the straight line which passes through the point (2, -2) and the point of intersection of the lines 5x-y=9 and x+6y=8 .

Find the equation of the straight line passing through the point (2, 5) and perpendicular to the line 2x+5y=31 .

Find the equation of the straight line which passes through the point (2, -9) and the intersection of the lines 2x+5y-8=0 and 3x-4y=35

Find the equation of a straight line: with slope 2 and y-intercept 3;

Find the equation of the straight line through (x_1, y_1) perpendicular to the line joining (x_2, y_2) and (x_3 , y_3) .

Find the equations of the straight lines joining the origin to the points of intersection of x^2+y^2-4x-2y=4 and x^2+y^2-2x-4y=4 .