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 PUBLICATION|Exercise Concept Applications Exercise 5.4|13 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.5|9 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.2|17 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

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.

What is the length of the focal distance from the point P(x_(1),y_(1)) on the parabola y^(2) =4ax ?

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

The lngth of the tangent from the point (1, 1) to the circle x^2 + y^2 + 4x + 6y + 1 = 0 is

Find the equation of line which is normal to the parabola x^(2)=4y and touches the parabola y^(2)=12x .

Find the length of the tangent from any point on the circule x^(2)+y^(2)-4x+6y-2=0 to the circle x^(2)+y^(2)-4x+6y+7=0

Find the equations of the tangents drawn from the point A(3, 2) to the circle x^2 + y^2 + 4x + 6y + 8 = 0

In one of the diameters of the circle, given by the equation x^(2) + y^(2) - 4x + 6y - 12 = 0 , is a chord of a circle S , whose center is at (-3 , 2) , then the radius of S is

The coordinates of the point on the parabola y^2=8x which is at a minimum distance from the circle x^2+(y+6)^2=1 are