Home
Class 12
MATHS
If the line passing through the focus S ...

If the line passing through the focus `S` of the parabola `y=a x^2+b x+c` meets the parabola at `Pa n dQ` and if `S P=4` and `S Q=6` , then find the value of `adot`

Text Solution

Verified by Experts

The correct Answer is:
`pm(5)/(48)`
The length of latus rectum of`y=ax^(2)+bx+c" is "1//|a|`. Now, the semi-latus rectum is the HM of SP and SQ.
Then, we have
`(1)/(SP)+(1)/(SQ)=(2)/(1//|2a|)`
`or4|a|=(1)/(4)+(1)/(6)=(5)/(12)`
`ora=pm(5)/(48)`
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

A line L passing through the focus of the parabola y^2=4(x-1) intersects the parabola at two distinct points. If m is the slope of the line L , then (a) -1 1 (c) m in R (d) none of these

A line L passing through the focus of the parabola (y-2)^(2)=4(x+1) intersects the two distinct point. If m be the slope of the line I,, then

A line L passing through the focus of the parabola y^2=4(x-1) intersects the parabola at two distinct points. If m is the slope of the line L , then -1 1 m in R (d) none of these

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Qa n dR , then find the midpoint of chord Q Rdot

If y=x+2 is normal to the parabola y^2=4a x , then find the value of adot

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Q and R , then find the midpoint of chord Q Rdot

Radius of the largest circle which passes through the focus of the parabola y^2=4x and contained in it, is

The normal to the parabola y^(2)=4x at P (1, 2) meets the parabola again in Q, then coordinates of Q are

Find the coordinates of the vertex and the focus of the parabola y^(2)=4(x+y) .

If the line x+y=a touches the parabola y=x-x^2, then find the value of adot