Higher Math 2nd Paper CQ-Dhaka Board-2021

Find the eccentricity of hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{16}=1$.

Find the equation of the parabola according to scenario-1.

Find the equation of an ellipse that the point $(4,0)$ lies on an ellipse according to scenario-2.

If the ellipse $\frac{x^{2}}{p}+\frac{y^{2}}{25}=1$ passes through the point $(6,4)$, find the length of major axis of the ellipse.

Vertex of parabola is $(1,2)$ and the parabola passes through the point $(3,-2)$, find the values of $\mathrm{a}, \mathrm{b}, \mathrm{c}$ according to scenario-1.

If the length of latus rectum of hyperbola is 10 units then find the equation of hyperbola according to scenario-2.

What will be the value of a when the roots of the equation $(a-1) x^{2}-(a+2) x+4=0$ are real and equal?

If $a=4, b=-2, c=0$ and $d=3$ of the equation $\varphi(x)=0$ and the roots are $\alpha, \beta, \gamma$ then find the value of $\sum \alpha^{2} \beta$.

If $a=0, b=1, c=-l$ and $d=m$ of the equation $\varphi(x)=0$. If the roots of the equation $\varphi(x)=0$ and $\psi(x)=0$ differ only by a constant then prove that, $l+\mathrm{m}+4=0$.

Prove that, $\cot ^{-1}(\tan 2 \varphi)+\cot ^{-1}(-\tan 3 \varphi)=\varphi$.

Solve that, $(2+\sqrt{3}) \mathrm{f}(2 \theta)=1-\mathrm{f}\left(\frac{\pi}{2}-2 \theta\right)$ according to stem.

Prove that $2 h\left(\frac{\sqrt{a-b}}{\sqrt{a+b}} \tan ^{\frac{\theta}{2}}\right)=\cos ^{-1} \frac{b+a f(\theta)}{a+b f(\theta)}$.

Define the resolved part of a force.

According to scenario-1; $\mathrm{O}$ is the incenter of triangle $A B C$ and three forces acting are in equilibrium. Show that,

$P_{1}{ }^{2}: P_{2}{ }^{2}: P_{3}{ }^{2}=(1+\cos A):(1+\cos B):(1+\cos$ C).

According to scenario-2 how much equal force is added with each of the two forces, the new resultant moves $8 \mathrm{~cm}$ away from the old resultant?