If the ellipse (x2/a2)+(y2/b2)=1 is rotated about centre in its own plane by 90° in clockwise direction then the point (a cos θ, b sin θ) becomes

Question

If the ellipse (x2/a2)+(y2/b2)=1 is rotated about centre in its own plane by 90° in clockwise direction then the point (a cos θ, b sin θ) becomes (A) (a cos θ,-b sin θ) (B) (b sin θ,-a cos θ) (C) (b sin θ, a cos θ) (D) none of these

Tardigrade Admin · Accepted Answer

Point P goes to Q. Its direction with respect to x-axis is q in original position. In new position y-axis will play the role of major axis so its inclination with negative direction of y-axis will be same. So, new coordinates will be (b sin θ,-a cos θ).

Q. If the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ is rotated about centre in its own plane by $9 0^{\circ}$ in clockwise direction then the point $(a cos θ, b sin θ)$ becomes

$(a cos θ, - b sin θ)$

$(b sin θ, - a cos θ)$

$(b sin θ, a cos θ)$

none of these

Point $P$ goes to $Q$ . Its direction with respect to $x$ -axis is $q$ in original position. In new position $y$ -axis will play the role of major axis so its inclination with negative direction of $y$ -axis will be same. So, new coordinates will be $(b sin θ, - a cos θ)$ .

Q. If the ellipse a2x2​+b2y2​=1 is rotated about centre in its own plane by 90∘ in clockwise direction then the point (acosθ,bsinθ) becomes

(acosθ,−bsinθ)

(bsinθ,−acosθ)

(bsinθ,acosθ)