The curves ` x^(3) -3xy^(2) = a and 3x^(2)y -y^(3)=b,` where a and b are constants, cut each other at an angle ofA. `(pi)/(3)`B. `(pi)/(4)`C. `(pi)/(2)`D. none of these

The curves ` x^(3) -3xy^(2) = a and 3x^(2)y -y^(3)=b,` where a and b a

1.	The curves ` x^(3) -3xy^(2) = a and 3x^(2)y -y^(3)=b,` where a and b are constants, cut each other at an angle ofA. `(pi)/(3)`B. `(pi)/(4)`C. `(pi)/(2)`D. none of these
Answer» Correct Answer - C The equation of the two curves are `C_(1) : x^(3) -3xy^(2) =a " " ` …(i) `C_(2): 3x^(2)y -y^(3)=b " " ` …(ii) Differentiating (i) and (ii) w.r.t. x, we get `((dy)/(dx))_(C_(1))=(x^(2)-y^(2))/(2xy) and ((dy)/(dx))_(C_(2)) = -(2xy)/(x^(2)-y^(2))` Clearly, `((dy)/(dx))_(C_(1)) xx((dy)/(dx))_(C_(2))= -1` So, the two curves intersect at right angle.

Discussion

No Comment Found

Related InterviewSolutions

f the normal at the point `P (at_1, 2at_1)` meets the parabola `y^2=4ax` aguin at `(at_2, 2at_2),` thenA. `t_(1)t_(2)= -1`B. `t_(2)= -t_(1) -(2)/(t_(1))`C. `2t_(1)=t_(2)`D. none of these
Let `P(2, 2) and Q(1//2, -1)` be two points on the parabola `y^(2)=2x`, The coordinates of the point R on the parabola `y^(2) =2x` where the tangent to the curve is parallel to the chord PQ, areA. `(2, -1)`B. `(1//8,1//2)`C. `(sqrt(2),1)`D. `(-sqrt(2),1)`
The tangent and normal at `P(t)`, for all real positive `t`, to the parabola `y^2= 4ax` meet the axis of the parabola in `T` and `G` respectively, then the angle at which the tangent at `P` to the parabola is inclined to the tangent at `P` to the circle passing through the points `P, T `and `G` isA. `tan^(-1)t^(2)`B. `cot^(-1)t^(2)`C. `tan^(-1)t`D. `cot^(-1)t`
If the curves `2x^(2)+3y^(2)=6 and ax^(2)+4y^(2)=4` intersect orthogonally, then a =A. 2B. 1C. 3D. none of these
The curves `ax^(2)+by^(2)=1 and Ax^(2)+B y^(2) =1` intersect orthogonally, thenA. `(1)/(a)+(1)/(A)=(1)/(b) + (1)/(B)`B. `(1)/(a)-(1)/(A)=(1)/(b) - (1)/(B)`C. `(1)/(a)+(1)/(b)=(1)/(B) - (1)/(A)`D. `(1)/(a)+(1)/(b)=(1)/(A) + (1)/(B)`
Find the condition for the following set of curves to intersectorthogonally:`(x^2)/(a^2)-(y^2)/(b^2)=1`and `x y=c^2``(x^2)/(a^2)+(y^2)/(b^2)=1`and `(x^2)/(A^2)-(y^2)/(B^2)=1.`
`" For a curve "(("length of normal"))/(("length of tangent"))` is equal toA. subtangentB. subnormalC. slope of tangentD. slope of normal
Let C be the curve `y^(3) - 3xy + 2 =0`. If H is the set of points on the curve C, where the tangent is horizontal and V is the set of points on the curve C, where the tangent is vertical, then H = … and V = … .A. `H={(x,y):y=0, x inR}, V={(1,1)} `B. `H={(x,y):x=0, y in R}, V={(1,1)} `C. `H=phi , V={(1,1)} `D. `H={(1,1)} , V={(x,y):y=0, x in R} `
The curves `x=y^(2) and xy =a^(3)` cut orthogonally at a point, then a =A. `(1)/(3)`B. 3C. 2D. `(1)/(2)`
The curves ` x^(3) -3xy^(2) = a and 3x^(2)y -y^(3)=b,` where a and b are constants, cut each other at an angle ofA. `(pi)/(3)`B. `(pi)/(4)`C. `(pi)/(2)`D. none of these

The curves ` x^(3) -3xy^(2) = a and 3x^(2)y -y^(3)=b,` where a and b are constants, cut each other at an angle ofA. `(pi)/(3)`B. `(pi)/(4)`C. `(pi)/(2)`D. none of these

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment