Home
Class 12
MATHS
Find the locus of the point of intersect...

Find the locus of the point of intersection of the perpendicular tangents of the curve `y^2+4y-6x-2=0` .

Text Solution

Verified by Experts

The correct Answer is:
2x+5=0
We know that perpendicular tangents meet at the directrix.
The given parabola is `y^(2)+4y-4x-2=0`
`or" "(y+2)^(2)=6(x+1)`
The equation of directrix is
`x+1=-(6)/(4)orx=-(5)/(2)`
`or" "2x+5=0`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.6|8 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.7|9 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.4|13 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

If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 is 120^0 and the product of perpendiculars drawn from the foci upon its any tangent is 9, then the locus of the point of intersection of perpendicular tangents of the hyperbola can be (a) x^2+y^2=6 (b) x^2+y^2=9 x^2+y^2=3 (d) x^2+y^2=18

The locus of the point of intersection of two perpendicular tangents to the ellipse (x^(2))/(9) +(y^(2))/(4)=1 is -

The locus of the point of intersection of a pair of perpendicular tangents to an ellipse is a/an-

Obtain the locus of the point of intersection of the tangent to the circle x^2 + y^2 = a^2 which include an angle alpha .

The curve be y=x^2 whose slopeof tangent is x, so find the point of intersection of the tangent and the curve.

The locus of the point of intersection of the tangents to the circle x^2+ y^2 = a^2 at points whose parametric angles differ by pi/3 .

Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola x^(2)-y^(2)=a^(2)" is " a^(2)(y^(2)-x^(2))=4x^(2)y^(2) .

Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola x^2-y^2=a^2 is a^2(y^2-x^2)=4x^2y^2dot

Find the locus of a point which moves so that the ratio of the lengths of the tangents to the circles x^2+y^2+4x+3=0 and x^2+y^2-6x+5=0 is 2: 3.

Tangent are drawn to the circle x^2+y^2=1 at the points where it is met by the circles x^2+y^2-(lambda+6)x+(8-2lambda)y-3=0,lambda being the variable. The locus of the point of intersection of these tangents is (a) 2x-y+10=0 (b) 2x+y-10=0 (c) x-2y+10=0 (d) 2x+y-10=0