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

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 ENGLISH|Exercise Section II - Assertion Reason Type|7 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|80 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|20 Videos

Similar Questions

Explore conceptually related problems

The values that m can take so that the straight line y=4x+m touches the curve x^(2)+4y^(2)=4 is

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

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

The number of values of a for which the lines 2x+y-1=0 , a x+3y-3=0, and 3x+2y-2=0 are concurrent is (a).0 (b) 1 (c) 2 (d) infinite

If the line y=mx+c touches the parabola y^(2)=4a(x+a) , then

Number of circle touching both the axes and the line x+y=4 is greater than or equal to : (a) 1 (b) 2 (c) 3 (d) 4

The angle of intersection between the curves x^(2) = 4(y +1) and x^(2) =-4 (y+1) is (a) pi/6 (b) pi/4 (c) 0 (d) pi/2

The line y=m x+1 is a tangent to the curve y^2=4x , if the value of m is (a) 1 (b) 2 (c) 3 (d) 1/2

The slope of the line touching both the parabolas y^2=4x and x^2=−32y is (a) 1/2 (b) 3/2 (c) 1/8 (d) 2/3

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=2 (c) x+y=2 (d) none of these

OBJECTIVE RD SHARMA ENGLISH-ELLIPSE-Section I - Solved Mcqs
  1. If tan alpha tan beta=-(a^(2))/(b^(2), then the chord joining two poin...

    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. If eccentric angle of a point on the ellipse x^(2)/6+y^(2)/2=1, whose ...

    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 the...

    Text Solution

    |

  10. A focus of an ellipse Is that the rigin. The directrix is the line x=4...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. If F1" and "F2 be the feet of perpendicular from the foci S1" and "S2 ...

    Text Solution

    |

  14. The area of the rectangle formed by the perpendicular from the center ...

    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

    |