Let a, b, c and d be non-zero numbers. If the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given lines are $4ax + 2ay + c = 0$ $(i)$ and $5bx + 2by + d = 0$ (ii).Multiply $(i)$ by $b$ and (ii) by $a$:$4abx + 2aby + bc = 0$ (iii)$5abx + 2

Vedclass · Accepted Answer

$3bc - 2ad = 0$

Vedclass · Answer

(A) Given lines are $4ax + 2ay + c = 0$ $(i)$ and $5bx + 2by + d = 0$ (ii).Multiply $(i)$ by $b$ and (ii) by $a$:$4abx + 2aby + bc = 0$ (iii)$5abx + 2aby + ad = 0$ (iv)Subtracting (iii) from (iv):$(5ab - 4ab)x + (ad - bc) = 0$ $\Rightarrow abx = bc - ad$ $\Rightarrow x = \frac{bc - ad}{ab}$.Substitute $x$ into (ii):$5b(\frac{bc - ad}{ab}) + 2by + d = 0 \Rightarrow \frac{5(bc - ad)}{a} + 2by + d = 0$.$2by = -d - \frac{5bc - 5ad}{a} = \frac{-ad - 5bc + 5ad}{a} = \frac{4ad - 5bc}{a}$.$y = \frac{4ad - 5bc}{2ab}$.The point $P(x, y)$ is in the fourth quadrant,so $x > 0$ and $y $\frac{bc - ad}{ab} = -(\frac{4ad - 5bc}{2ab}) \Rightarrow \frac{bc - ad}{ab} = \frac{5bc - 4ad}{2ab}$.$2(bc - ad) = 5bc - 4ad \Rightarrow 2bc - 2ad = 5bc - 4ad$.$2ad = 3bc \Rightarrow 3bc - 2ad = 0$.

List$-I$	List$-II$
$(P)$ Stephen reaction	$(1)$ Toluene $\xrightarrow{\substack{\text { (i) } CrO _2 Cl _2 / CS _2 \\ \text { (ii) } H _3 O +}}$
$(Q)$ Sandmeyer reaction	$(2)$ Benzoic acid $\xrightarrow{\substack{\text { (i) } PCl _5 \\ \text { (iii) } NH _3 \\ \text { (iii) } P _4 O _{10}, \Delta}}$
$(R)$ Hoffmann bromamide degradation reaction	$(3)$ Nitrobenzene $\xrightarrow{\begin{array}{l}\text { (i) } Fe , HCl \\ \text { (ii) } HCl , NaNO _2 \\ \text { (273-278 K), } H _2 O \end{array}}$
$(S)$ Cannizzaro reaction	$(4)$ Toluene $\xrightarrow{\begin{array}{l}\text { (i) } Cl _2 / hv , H _2 O \\ \text { (ii) } \text {Tollen 's reagent } \\ \text { (iii) } SO _2 Cl _2 \\ \text { (iv) } NH _3\end{array}}$
	$(5)$ Aniline $\xrightarrow{\substack{\text { (i) }\left( CH _3 CO \right)_2 O , \text { Pyridine } \\ \text { (ii) } HN O _3 H _{2} SO _4, 288 K \\ \text { (iii) } aq . NaOH }}$

Let $a, b, c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4ax + 2ay + c = 0$ and $5bx + 2by + d = 0$ lies in the fourth quadrant and is equidistant from the two coordinate axes,then

Similar Questions

What type of life cycle in plants is indicated by the given figure?

If $\int \sec ^2 x \operatorname{cosec}^4 x \, dx = -\frac{1}{3} \cot ^3 x + k \tan x - 2 \cot x + C$,then $k$ is equal to

If $\lim _{x \rightarrow 0}\left(\frac{\cos 4 x+a \cos 2 x+b}{x^4}\right)$ is finite,then the values of $a, b$ are respectively :

For positive numbers $x, y, \text{ and } z$,the numerical value of the determinant $\left| \begin{array}{ccc} 1 & \log_x y & \log_x z \\ \log_y x & 1 & \log_y z \\ \log_z x & \log_z y & 1 \end{array} \right|$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module