Home
Class 12
MATHS
Circles drawn on the diameter as focal ...

Circles drawn on the diameter as focal distance of any point lying on the parabola `x^(2)-4x+6y+10 =0` will touch a fixed line whose equation is a. y=1 b. y=-1 c. y=2 d. y=-2

Text Solution

Verified by Experts

The correct Answer is:
y+1=0
`x^(2)-4x+6y+10=0`
`or" "x^(2)-4x+4=-6-6y`
`or" "(x-2)^(2)=-6(y+1)`
The circle drawn on focal distance as diameter always touches the tangent drawn to the parabola at vertex.
Thus, the circle will touch the line y+1=0.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE ENGLISH|Exercise Concept Applications Exercise 5.4|13 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise Concept Applications Exercise 5.5|9 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise Concept Applications Exercise 5.2|17 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

The focal distance of the point (9,6) on the parabola y^(2)=4x is

The focal distance of the point (9,6) on the parabola y^(2)=4x is

Prove that the focal distance of the point (x ,y) on the parabola x^2-8x+16 y=0 is |y+5|

Prove that the focal distance of the point (x ,y) on the parabola x^2-8x+16 y=0 is |y+5|

Circles are drawn with diameter being any focal chord of the parabola y^2-4x-y-4=0 with always touch a fixed line. Find its equation.

Find the points on the parabola y^2-2y-4x=0 whose focal length is 6.

Find the points on the parabola y^2-2y-4x=0 whose focal length is 6.

If the line y=mx+c touches the parabola y^(2)=4a(x+a) , then

If the line y=mx+c touches the parabola y^(2)=4a(x+a) , then

The line 4x+6y+9 =0 touches the parabola y^(2)=4ax at the point