SATHEE: Straight Line Question 232

Straight Line Question 232

Question: The equation $ {{(x^{2}-a^{2})}^{2}}{{(x^{2}-b^{2})}^{2}}+c^{4}{{(y^{2}-a^{2})}^{2}}=0 $ represents $ (c\ne 0) $

Options:

A) 8 points

B) Two circles

C) 4 lines

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $ {{(x^{2}-a^{2})}^{2}}{{(x^{2}-b^{2})}^{2}}+c^{4}{{(y^{2}-a^{2})}^{2}}=0 $ This being the sum of two perfect squares, each term must be zero. Hence, we get $ {{(x^{2}-a^{2})}^{2}}{{(x^{2}-b^{2})}^{2}}=0 $ or $ (x^{2}-a^{2})(x^{2}-b^{2})=0 $ or $ (x-a)(x+a)(x-b)(x+b)=0 $ ? (1) and $ c^{4}{{(y^{2}-a^{2})}^{2}}=0 $ or $ c^{2}(y^{2}-a^{2})=0 $ or $ c^{2}(y+a)(y-a)=0 $ ? (2) Equation no. (1) Holds good for $ x=\pm a $ or $ x=\pm b $ Equation no. (2) Is satisfied by $ y=\pm a $ As both of these should be simultaneously satisfied, the give equation represents 8 points which we get as a result of different combinations of (1) and (2), namely $ (\pm a,\pm a),(\pm b,\pm a). $

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Straight Line Question 232

Question: The equation $ {{(x^{2}-a^{2})}^{2}}{{(x^{2}-b^{2})}^{2}}+c^{4}{{(y^{2}-a^{2})}^{2}}=0 $ represents $ (c\ne 0) $

Options:

Answer:

Solution:

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