Home
Class 12
MATHS
The number of values of c such that the ...

The number of values of `c` such that the straight line `y=4x+c` touches the curve `(x^2)/4+(y^2)/1=1` is

A

0

B

1

C

2

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
C
We know that the line y = mx + c touches the curve `x^(2)/a^(2) + y^(2)/b^(2) = 1` iff `c^(2) = a^(2) m^(2) + b^(2)`.
Here, `a^(2) = 4, b^(2) = 1, m = 4`
`therefore c^(2) = 64 + 1 rArr c = pm sqrt(65)`
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|7 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA|Exercise Exercise|82 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|20 Videos

Similar Questions

Explore conceptually related problems

The number of values of c such that the straight line y=4x+c touches the curve (x^(2))/(4)+y^(2)=1 is k then, k is

The number of values of c such that the straight line 3x+4y=c touches the curve (x^(4))/(2)=x+y is

Prove that the straight line y=x+sqrt((7)/(12)) touches the ellipse.3x^(2)+4y^(2)=1

The line y = 4x + c touches the hyperbola x^(2) - y^(2) = 1 if

A straight line x=y+2 touches the circle 4(x^(2)+y^(2))=r^(2), The value of r is:

Find the condition that the straight line y = mx + c touches the hyperbola x^(2) - y^(2) = a^(2) .

If the line x+y=0 touches the curve 2y^(2)=ax^(2)+b at (1,-1), then

The number of circles that touch all the straight lines x+y-4=0, x-y+2=0 and y=2 , is

OBJECTIVE RD SHARMA-ELLIPSE-Section I - Solved Mcqs
  1. If tantheta1.tantheta2=a^2/b^2 then the chord Joining two points theta...

    Text Solution

    |

  2. The locus of point of intersection of tangents to an ellipse x^2/a^2+y...

    Text Solution

    |

  3. The number of values of c such that the straight line y=4x+c touches t...

    Text Solution

    |

  4. If P(x ,y) is any point on the ellipse 16 x^2+25 y^2=400 and f1=(3,...

    Text Solution

    |

  5. An ellipse slides between two perpendicular straight lines. Then id...

    Text Solution

    |

  6. The sum fo the squares of the perpendicular on any tangent to the elli...

    Text Solution

    |

  7. The eccentric angle of a point on the ellipse x^(2)/6 + y^(2)/2 = 1 wh...

    Text Solution

    |

  8. If any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 intercepts e...

    Text Solution

    |

  9. The ellipse x^2+""4y^2=""4 is inscribed in a rectangle aligned with...

    Text Solution

    |

  10. A focus of an ellipse is at the origin. The directrix is the line x =4...

    Text Solution

    |

  11. In an ellipse, the distances between its foci is 6 and minor axis is 8...

    Text Solution

    |

  12. The tangent at a point P(acostheta,bsintheta) of the ellipse (x^2)/(a^...

    Text Solution

    |

  13. if F(1) and F(2) be the feet of the perpendicular from the foci S(1) a...

    Text Solution

    |

  14. The area of the rectangle formed by the perpendiculars form the centre...

    Text Solution

    |

  15. Find the slope of a common tangent to the ellipse (x^2)/(a^2)+(y^2)/(b...

    Text Solution

    |

  16. P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with AA ' ...

    Text Solution

    |

  17. Find the equation of an ellipse the distance between the foci is 8 ...

    Text Solution

    |

  18. The line x = at^(2) meets the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 in...

    Text Solution

    |

  19. On the ellipse 4x^2+9y^2=1, the points at which the tangents are paral...

    Text Solution

    |

  20. If circumcentre of an equilateral triangle inscribed in x^(2)/a^(2) + ...

    Text Solution

    |