Question
if $\left(a^2+b^2\right)\left(x^2+y^2\right)= (ax + by)^2 ;$ prove that $\frac{a}{x}=\frac{b}{y}$
✓
Answer
Given $\left(a^2+b^2\right)\left(x^2+y^2\right)=(a x+b y)^2$
$a^2 x^2+a^2 y^2+b^2 x^2+b^2 y^2+b^2 y^2+2 a b x y $
$a^2 y^2+b^2 x^2-2 a b x y=0 \\ (a y-b x)^2=0 $
$ \text { ay - bx }=0 $
$ \text { ay }=\text { bx } $
$ \frac{a}{x}=\frac{b}{y}$
$a^2 x^2+a^2 y^2+b^2 x^2+b^2 y^2+b^2 y^2+2 a b x y $
$a^2 y^2+b^2 x^2-2 a b x y=0 \\ (a y-b x)^2=0 $
$ \text { ay - bx }=0 $
$ \text { ay }=\text { bx } $
$ \frac{a}{x}=\frac{b}{y}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the solution set of the following inequalities and draw the graph of their solutions sets :
| x - 1 | > 3
| x - 1 | > 3
Find two consecutive even natural numbers such that the sum of their squares is $340$.
→Prove that $\frac{\cot A+\operatorname{cosec} A-1}{\cot A-\operatorname{cosec} A+1}=\frac{1+\cos A}{\sin A}$
→If $A=\left[\begin{array}{ll}4 & 2 \\ 1 & 1\end{array}\right]$ Find $(A-2I)(A - 3I)$
→If $A=\left[\begin{array}{cc}3 & -5 \\ -4 & 2\end{array}\right]$ find $A^2-5 A-14$ I
Where $I$ is unit matrix of order $2 \times 2$
→Where $I$ is unit matrix of order $2 \times 2$
A retailer in Jaipur (Rajasthan) buys goods from a dealer in Alwar (Rajasthan) at a discount of $20\%$. The retailer sells it to a customer in Jaipur at the printed price. If the printed price of the goods is ₹ $16,000$ and the GST rate is $8 \%$, calculate :
(i) the price paid by the customer for the goods.
(ii) the CGST and the SGST payable by the retailer in Jaipur to the government.
→(i) the price paid by the customer for the goods.
(ii) the CGST and the SGST payable by the retailer in Jaipur to the government.
Second term of a Geometric Progression is $6$ and its fifth term is $9$ times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.
→In the figure, a circle touches all the four sides of a quadrilateral ABCD with AB = 6 cm, BC = 7 cm and CD = 4 cm. What is the length of AD?
There are $50$ students in a class in which $40$ are boys and rest are girls. The average weight of the class is $44$ kgs and the average weight of the girls is $40$ kgs. Find the average weight of the boys.
→₹ $ 8,000$ and ₹ $ 10,000$ were invested in ₹ $ 100$ shares giving dividends $12 \%$ and $8 \%$ respectively. The dividends are collected and all the shares are sold at a loss $2 \%$ and $3 \%$ respectively on the investment. Find (i) the dividend collected (ii) the total sale proceeds (iii) gain $\%$ on the whole transaction.
→