Home
Class 12
MATHS
Show that the straight line (x)/(a)+(y)/...

Show that the straight line `(x)/(a)+(y)/(b)=2` touches the curve `((x)/(a))^(3)+((y)/(b))^(3)=2`, find the coordinates of the point of contact.

Text Solution

Verified by Experts

The correct Answer is:
`(a,b)`
Doubtnut Promotions Banner Mobile Dark
|

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

Prove that the line x+y=3a touches the curve x^(3)+y^(3)=3axy, find the coordinnates of the points of contact.

Show that the line (x)/(a)+(y)/(b)=1 touches the curve y= be ^(-(x)/(a)) at the point where it crosses the y-axis.

Knowledge Check

  • If the line 2x+sqrt(6)y=2 is a tangent to the hyperbola x^(2)-2y^(2)=4 , then the coordinates of the point of contact are -

    A
    `(4,-sqrt(6))`
    B
    `(7, -2sqrt(6))`
    C
    `(2, 3)`
    D
    `(sqrt(6), 1)`

  • If the tangent to the parabola y= x^(2) + 6 at the point (1, 7) also touches the circle x^(2) + y^(2) + 16x + 12y + c =0 , then the coordinates of the point of contact are-

    A
    (-1, -2)
    B
    (2, 3)
    C
    (6, -7)
    D
    (-6, -7)

    • Similar Questions

    Explore conceptually related problems

    If y=mx+c is the tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at any point on it, show that c^(2)=a^(2)m^(2)+b^(2). Find the coordinates of the point of contact.

    If the straight line (x)/(h)+(y)/(k)=1 touches the curve (x/a)^(n)+((y)/(b))^(n)=1 , then show that ((a)/(h))^((n)/(n-1))+((b)/(k))^((n)/(n-1))=1

    Find the condition that the straight line lx+my=n touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

    If x/a+y/b=sqrt2 touches the ellipses x^2/a^2+y^2/b^2=1 , then find the ecentricity angle theta of point of contact.

    Show that the straight line (a+2b)x+(a-3b)y+b-a=0 always passes through a fixed point , find the cootdinates of that fixed point.

    Find the equation of tangent to the circle x^(2)+y^(2)=a^(2) at the point (a cos theta, a sin theta) . Hence , show that the line y=x+a sqrt(2) touches the given circle,Find the coordinats of the point of contact.

    Home
    Profile