If x\over y = (a + 2)\over (a - 2), then find the value of (x² - y²)\over (x² + y²)
WBBSE
Class X
Mathematics
Ratio And Proportion
03 Mark
2025
\text{x}\over \text{y} = \text{a + 2}\over \text{a - 2}
squaring both side
or, \text{x²}\over \text{y²}= \text{(a + 2)²}\over \text{(a - 2)²}
Applying componendo and dividendo
\text{x² + y²}\over \text{x² - y²} = \text{(a + 2)² + (a - 2)²}\over \text{(a + 2)² + (a - 2)²}
= \text{(a + 2)² + (a - 2)²}\over \text{(a + 2)² - (a - 2)²}
= \text{2(a² + 4)}\over \text{8a}
= \text{a² + 4}\over \text{4a}
∴ \text{x² - y²}\over \text{x² + y²} = \text{4a}\over \text{a² + 4}
Related Questions
More WBBSE Moderate level questions
1/12
Q.
Find the ratio of length of radius and perimeter of a circle
A.
The perimeter (circumference) of a circle is given by: C = 2πr...
Q.
If a : 2 = b : 5 then how many % of b is...
A.
(c) 40 Explanation: ⇒ a / 2 = b / 5 ⇒...
Q.
If a, b, c are in continued proportion, then prove that, 1/b=1/(b-a) +1/(b-c)
A.
a, b, c are in continued proportion ⇒ b² = ac LHS:...
Q.
If the fourth and fifth of the five numbers in continued proportion are 54 and...
A.
Let the continued proportion be a, ak, ak², ak3, ak4 Given: ak3...
Q.
If (b + c – a)x = (c + a – b)y = (a +...
A.
Given: (b + c - a)x = (c + a - b)y...
Q.
Find the mean proportion of xy² and xz²
A.
Mean proportion of two numbers a and b is given by: Substituting...
Q.
If \dfrac{a}{1-a}+\dfrac{b}{1-b}+\dfrac{c}{1-c}=1, then find the value of \dfrac{1}{1-a}+\dfrac{1}{1-b}+\dfrac{1}{1-c}.
A.
= 1 or, = 1 + 1 + 1 + 1 or,...
Q.
If a : b = b : c, prove that \frac{\text{abc(a + b + c)³}}{\text{(ab...
A.
Given: a : b = b : c ⇒ ac = b²...
Q.
Find the ratio of the cost price and selling price of an article which is...
A.
Let the cost price (CP) be 100 Given profit = 25% of...
Q.
If (3x − 2y) : (3x + 2y) = 4 : 5 then what is...
A.
(3x − 2y)/(3x + 2y) = 4/5 ⇒ 5(3x − 2y) =...
Q.
The corresponding sides of two similar triangles are ____.
A.
Proportional Explanation : When two triangles are similar, their shapes are the...
Q.
State True or False: The compound ratio of 2ab : c², bc : a² and...
A.
True Explanation 2ab : c², bc : a² and ca : 2b2...