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Mathematical Operators

Add x2-y2 -1,...

Question

Add $x^{2} - y^{2} - 1, y^{2} - 1 - x^{2}$ , and $1 - x^{2} - y^{2}$
[2 marks]

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Solution

Addition of $x^{2} - y^{2} - 1, y^{2} - 1 - x^{2}$ , and $1 - x^{2} - y^{2} = x^{2} - y^{2} - 1 + y^{2} - 1 - x^{2} + 1 - x^{2} - y^{2}$
$= x^{2} - x^{2} - x^{2} - y^{2} + y^{2} - y^{2} - 1 - 1 + 1$
$= (1 - 1 - 1) x^{2} + (- 1 + 1 - 1) y^{2} - 1 - 1 + 1$
$= - x^{2} - y^{2} - 1$
(2 marks)

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Question 70

From the sum of $x^{2} - y^{2} - 1, y^{2} - x^{2} - 1$ and $1 - x^{2} - y^{2}$ , subtract $- (1 + y^{2}) .$

Q. Find the angle of intersection of the following curves

(i) y² = x and x² = y
(ii) y = x² and x² + y² = 20
(iii) 2y²= x³ and y² = 32x
(iv) x²+ y² − 4x − 1 = 0 and x² + y² − 2y − 9 = 0
(v)

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

and x² + y² = ab
(vi) x² + 4y² = 8 and x² − 2y² = 2
(vii) x² = 27y and y² = 8x
(viii) x² + y² = 2x and y² = x

Q. Find the angle of intersection of the following curves:

(i) y² = x and x² = y [NCERT EXEMPLAR]
(ii) y = x² and x² + y² = 20
(iii) 2y²= x³ and y² = 32x
(iv) x²+ y² − 4x − 1 = 0 and x² + y² − 2y − 9 = 0
(v)

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

and x² + y² = ab
(vi) x² + 4y² = 8 and x² − 2y² = 2
(vii) x² = 27y and y² = 8x
(viii) x² + y² = 2x and y² = x
(ix) y = 4 − x² and y = x² [NCERT EXEMPLAR]

Q. Add the following

x^{2} + y^{2} - z^{2}

{- x}^{2} - y^{2} + z^{2}

Q. From the sum of

x^{2} - y^{2} - 1, y^{2} - x^{2} - 1

1 - x^{2} - y^{2}

- (1 + y^{2}) .

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