Question

The curve y*2=ux*2+v passes through the point p(2,3) and dy/dx=4. find the values of u and v​

Answer 1

Given: the curve $y^{2}=ux^{2}+v$ passes through the point $P\:(2,3)$ and $\frac{dy}{dx}=4$

To find: the values of $u$ and $v$

Solution:

• Given, $y^{2}=ux^{2}+v$

• Differentiating both sides w. r. to $x$, we get
• $\quad 2y\frac{dy}{dx}=2ux$
• $\Rightarrow y\frac{dy}{dx}=ux$

• Since the curve passes through the point $(2,3)$ and $\frac{dy}{dx}=4$,
• $\quad 3\times 4=u\times 2$
• $\Rightarrow u=6$

• Putting $u=6$ and with condition of passing through $(2,3)$ from the curve, we get
• $\quad 3^{2}=6\times 2^{2}+v$
• $\Rightarrow 9=6\times 4+v$
• $\Rightarrow v=9-24$
• $\Rightarrow v=-15$

Answer:

• the value of $u$ is $6$
• the value of $v$ is $(-15)$