Doubt from coordinate geometry

ques 27 and 28

doubt ques 1,4,5,6,7for 1i am getting two values of b but answer says zero.for 5 iam getting 2 as answer but the answer is 4.for 6 i am getting the area of triangleABC 25squnits,so a should be 15 but the ans given is 9.

Q27) i think the options given are a bit incorrect

This should be the answer

Once confirm this answer from the solution given at the back , because sometimes in cengage the option are given wrong but solution is correct . Here in option A they have written OSA and there is no explanation to what S is , and if S is neglected then option A and B will be same , so i think maybe there was some printing error

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For 4th I’m getting 3

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Yes sir it is correct

sir can you please explain how it reached that step

Sir I have a doubt

In this ques what is wrong in my method

Sir for ques 28 can we say that two parts are congruent then they are of same area. Sir I did this by area under curve

For 6.14 How can you be confirmed that it is A standard ellipse . What you have done is just shifting of the centre in the standard ellipse equation . But its not necessary that ellipse is perfectly horizontal. It can be slanted too.