AP EAMCET · Maths · Application of Derivatives
The equation of the curve passing through \((1,2)\) and whose tangent at any point \((x, y)\) makes an angle \(\tan ^{-1}(2 x+3 y)\) with the \(X\)-axis is .........
- A \(6 x+9 y+2=26 e^{3 x-3}\)
- B \(6 x+9 y-2=26 e^{3 x-3}\)
- C \(6 x+9 y+2=26 e^{3 x+3}\)
- D \(6 x+9 y-2=26 e^{3 x+3}\)
Answer & Solution
Correct Answer
(A) \(6 x+9 y+2=26 e^{3 x-3}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}=(1,2)\) \[ \begin{aligned} \text { Inclination }(\theta) & =\tan ^{-1}(2 x+3 y) \\ \tan \theta & =2 x+3 y \\ \therefore \quad \text { Slope }(m) & =\tan \theta \end{aligned} \]…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\int_0^4 \frac{x+2}{\sqrt{4 x-x^2}} d x=\)AP EAMCET 2022 Medium
- The range of \(\operatorname{Sin}^{-1} x+\operatorname{Cos}^{-1} x+\operatorname{Tan}^{-1} x\) isAP EAMCET 2017 Easy
- If a line makes angles \(90^{\circ}, 135^{\circ}\) and \(45^{\circ}\) with the positive \(X, Y\) and \(Z\) axis respectively, then its direction cosines areAP EAMCET 2021 Easy
- \(2 x-3 y+1=0\) and \(4 x-5 y-1=0\) are the equations of two diameters of the circle \(S \equiv x^2+y^2+2 g x+2 f y-11=0\). Q and R are the points of contact of the tangents drawn from the point \(P(-2,-2)\) to this circle. If C is the centre of the circle \(S=0\), then the area (in square units) of the quadrilateral \(P Q C R\) isAP EAMCET 2024 Hard
- \(\tan \frac{\pi}{5}+2 \tan \frac{2 \pi}{5}+4 \cot \frac{4 \pi}{5}=\)AP EAMCET 2019 Easy
- If the function \(f(x)=a x^3+b x^2+11 x-6\) satisfies the conditions of Rolle's theorem in \([1,3]\) and \(f^{\prime}\left(2+\frac{1}{\sqrt{3}}\right)=0\), then \(a+b=\)AP EAMCET 2019 Easy
More PYQs from AP EAMCET
- In a potentiometer, a wire of length having resistance is used. A battery of and a resistor of are connected in series to the wire. If an unknown battery of emf balances the potentiometer at , then the value of isAP EAMCET 2018 Easy
- When a vehicle of mass \(m\) is moving with a velocity \(v\) over a concave over-bridge of radius of curvature \(r\), the thrust on the road at the lowest point on the bridge will beAP EAMCET 2021 Hard
- A region contains a uniform electric field \(\mathbf{E}=(10 \hat{\mathbf{i}}+30 \hat{\mathbf{j}}) \mathrm{Vm}^{-1} . A\) and \(B\) are two points in the field at \((1,2,0) \mathrm{m}\) and \((2,1,3) \mathrm{m}\), respectively. The work done when a charge of \(0.8 \mathrm{C}\) moves from \(A\) to \(B\) in a parabolic path isAP EAMCET 2016 Medium
- The relation between the coefficient of real expansion \(\left(\gamma_r\right)\) and coefficient of apparent expansion \(\left(\gamma_a\right)\) of a liquid and the coefficient of linear expansion \(\left(\alpha_g\right)\) of the material of the container isAP EAMCET 2005 Hard
- The sides of the rectangle of greatest area that can be inscribed in the ellipse \(x^2+4 y^2=64\) are :AP EAMCET 2006 Hard
- The drug used for relieving tension isAP EAMCET 2018 Easy