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Question No for 3 Mathematics


Compute space open parentheses 1 space plus fraction numerator 3 over denominator 1 plus fraktur i end fraction close parentheses squared space
space space straight A. fraction numerator negative 8 over denominator 2 end fraction minus 15 over 2 fraktur i
straight B.4 minus 15 over 2 fraktur i
straight C.17 over 2 minus 15 over 2 fraktur i
straight D.4

Answer for question no 3


straight B.4 minus 15 over 2 fraktur i

Solution for question no 3

open parentheses 1 space plus fraction numerator 3 over denominator 1 plus fraktur i end fraction close parentheses squared space equals open parentheses fraction numerator 1 plus fraktur i space plus 3 over denominator 1 plus fraktur i end fraction close parentheses squared space
open parentheses fraction numerator 4 space plus fraktur i over denominator 1 space plus fraktur i end fraction close parentheses squared space space equals fraction numerator 4 space plus fraktur i over denominator 1 space plus fraktur i end fraction cross times fraction numerator 4 space plus fraktur i over denominator 1 space plus fraktur i end fraction
fraction numerator 16 space plus 8 fraktur i minus 1 over denominator 1 plus fraktur i space plus fraktur i minus 1 end fraction equals fraction numerator 8 fraktur i space plus 15 over denominator 2 fraktur i end fraction
4 space plus fraction numerator 15 over denominator 2 fraktur i end fraction space
4 space plus fraction numerator 15 over denominator 2 fraktur i end fraction space cross times fraktur i over fraktur i equals
4 space minus 15 over 2 fraktur i space space space since space fraktur i cross times fraktur i equals negative 1
Answer space Option space straight B

Question No for 4 Mathematics

Find the centre and the radius of the circle


8 space straight x squared space plus space 8 space straight y squared space minus 24 straight x space minus 40 straight y space plus 18 space equals 0

straight A. left parenthesis bevelled fraction numerator 3 over denominator 2 comma space begin display style bevelled 5 over 2 end style end fraction right parenthesis space and space straight r space equals space bevelled 3 over 2
straight B. left parenthesis negative bevelled 3 over 2 comma space bevelled 5 over 2 right parenthesis space and space straight r space equals bevelled 5 over 2
straight C. left parenthesis bevelled fraction numerator 3 over denominator 2 comma space minus begin display style bevelled 5 over 2 end style end fraction right parenthesis space and space straight r space equals bevelled 3 over 2
straight D. left parenthesis bevelled fraction numerator 3 over denominator 2 comma space begin display style bevelled 5 over 2 end style end fraction right parenthesis space and space straight r space equals bevelled 5 over 2


Answer for question no 4

straight D. left parenthesis bevelled fraction numerator 3 over denominator 2 comma space begin display style bevelled 5 over 2 end style end fraction right parenthesis space and space straight r equals bevelled 5 over 2

Solution for question no 4



8 space straight x to the power of 2 space space end exponent plus space 8 space straight y squared space minus 24 straight x space minus 40 straight y space plus 18 space equals 0
8 left parenthesis space straight x to the power of 2 space end exponent plus space straight y squared space minus 3 straight x space minus 5 straight y space equals space minus 18
straight x squared plus straight y squared minus 3 straight x minus 5 straight y equals negative bevelled 18 over 8

Using general eaquation of circle


open parentheses straight x minus straight a close parentheses squared space plus left parenthesis straight y minus straight b right parenthesis squared equals straight r squared space

Where a and b is the centre of the circle and r is the radius.

Making the above equation a perfect square, we will get


left parenthesis straight x minus bevelled 3 over 2 right parenthesis squared space plus left parenthesis straight y minus bevelled fraction numerator 5 over denominator 2 right parenthesis squared space equals space minus begin display style bevelled 18 over 8 end style plus left parenthesis begin display style bevelled 3 over 2 end style right parenthesis end fraction squared plus bevelled fraction numerator left parenthesis 5 over denominator 2 end fraction right parenthesis squared comma space

From the above equation, the centre of the circle is bevelled 3 over 2 space and space bevelled 5 over 2


straight r squared equals negative bevelled 18 over 8 space plus bevelled 9 over 4 plus bevelled 25 over 4
straight r squared space equals fraction numerator 68 minus 18 over denominator 8 end fraction comma space straight r to the power of 2 space end exponent equals 50 over 8
straight r equals square root of bevelled 50 over 8 end root space rightwards double arrow straight r space equals bevelled fraction numerator square root of 2 over denominator square root of 2 end fraction space space space straight x bevelled fraction numerator square root of 25 over denominator square root of 4 end fraction
straight r equals bevelled 5 over 2
left parenthesis bevelled fraction numerator 3 over denominator 2 space comma end fraction bevelled fraction numerator 5 over denominator 2 right parenthesis space and space straight r space equals begin display style bevelled fraction numerator 5 over denominator 2 space end fraction end style end fraction

A n s w e r space i s space Option space. straight D