Home
Class 12
MATHS
Find the equation of the normal to the p...

Find the equation of the normal to the parabola `y^(2)=4ax` at a point `(x_(1),y_(1))` on it. Show that three normal can be drawn to a parabola from an external point.

Text Solution

Verified by Experts

The correct Answer is:
`y_(1)(x-x_(1))+2a(y-y_(1))=0`
Promotional Banner

Topper's Solved these Questions

  • TANGENT AND NORMAL

    CHHAYA PUBLICATION|Exercise A MULTIPLE CORRECT ANSWER TYPE|5 Videos

  • TANGENT AND NORMAL

    CHHAYA PUBLICATION|Exercise INTEGER ANSWER TYPE|5 Videos

  • TANGENT AND NORMAL

    CHHAYA PUBLICATION|Exercise SHORT ANSWER TYPE QUESTIONS|42 Videos

  • STRAIGHT LINE IN THREE DIMENSINAL SPACE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination|19 Videos

  • TRANSFORMATIONS OF SUMS AND PRODUCTS

    CHHAYA PUBLICATION|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

The equation of the normal to the parabola y^(2) =4ax at the point (at^(2), 2at) is-

Find the equation of normal to the hyperbola 4x^(2)-9y^(2)=36 , at the point (1,2)

Find the equations of the tangent and normal to the parabola y^(2) = 4ax at the point (at^(2) , 2at).

Find the equation of tangents drawn to the parabola y=x^2-3x+2 from the point (1,-1)dot

Find the equation of normal to the parabola y^(2)=4x , paralle to the straight line y=2x .

Find the equation of the normal to the hyperbola 3x^(2)-4y^(2)=12 at the point (x_(1),y_(1)) on it. Hence, show that the straight line x+y+7=0 is a normal to the hyperbola. Find the coordinates of the foot of the normal.

Find the equations of normal to the parabola y^2=4a x at the ends of the latus rectum.

The slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

Length of the shortest normal chord of the parabola y^2=4ax is

Find the locus of the midpoint of normal chord of parabola y^2=4a xdot

CHHAYA PUBLICATION-TANGENT AND NORMAL -LONG ANSWER TYPE QUESTIONS
  1. The equation of the tangent to the curve y=a+bx+cx^() where it meet th...

    Text Solution

    |

  2. If x(1) and y(1) be the intercepts on the x and y-axis respectively of...

    Text Solution

    |

  3. Show that the length of the portion of the tangent to the curve x^((2)...

    Text Solution

    |

  4. Show that the sum of the intercept on the coordinates axes of tangent ...

    Text Solution

    |

  5. If h and k be the intercept on the coordinates axes of tangent to the ...

    Text Solution

    |

  6. Find the equation of the normal to the parabola y^(2)=4ax at a point (...

    Text Solution

    |

  7. Find the coodition that the straight line lx+my+n=0 is a normal to the...

    Text Solution

    |

  8. Find the coodition that the straight line lx+my+n=0 is a normal to the...

    Text Solution

    |

  9. If the line lx+my=1 be a normal to the hyperbola (x^(2))/(a^(2))-(y...

    Text Solution

    |

  10. If the striaht line lx+my=1 is a normal to the parbaola y^(2)=4ax then...

    Text Solution

    |

  11. If the line lx+my=1 is normal to the hyperbola (x^(2))/(9)-(y^(2))/(4)...

    Text Solution

    |

  12. Show that the line (ax)/(3)+(by)/(4)=c be a normal to the ellipse (x^2...

    Text Solution

    |

  13. If the line x cos alpha+ y sin alpha=p be a normal to the hyperbola b^...

    Text Solution

    |

  14. Show that the normal to the curve x=3 cos theta- cos^(2) theta, y= 3 s...

    Text Solution

    |

  15. Show that the normal at any point theta to the curve x=a(cos theta+ th...

    Text Solution

    |

  16. Show that the normal to the rectangular hyperbola xy=c^(2) at point t ...

    Text Solution

    |

  17. The angle between the two tangents drawn from a point p to the circle ...

    Text Solution

    |

  18. Find the equation of tangent to the curve xy^(2)=4(4-x) where it meet ...

    Text Solution

    |

  19. Find the slope of normal to the ellipse , (x^(2))/(a^(2))+(y^(2))/(b^...

    Text Solution

    |

  20. Find the equation of the tangent to the curve x^((2)/(3))+y^((2)/(3))=...

    Text Solution

    |