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India
Class X

Systems of linear and non-linear equations

Interactive practice questions

Consider the hyperbola $y=\frac{3}{x}$y=3x and the line $y=5$y=5.

a

To solve for the point of intersection of the hyperbola and the line, Laura forms the equation $\frac{3}{x}=5$3x=5. At how many points will the two graphs intersect?

b

Solve for the $x$x-coordinate of the point of intersection.

c

Hence state the coordinates of the point of intersection in the form $\left(x,y\right)$(x,y).

Easy
3min

Consider the hyperbola $xy=2$xy=2 and the straight line $y=x+6$y=x+6.

Easy
1min

Consider the circle with equation $x^2+y^2=22$x2+y2=22 and the line with equation $y=2$y=2.

Easy
5min

The parabola $y=x^2+1$y=x2+1 has been graphed on the number plane.

State the minimum value of $k$k such that the line $y=k$y=k has at least one point of intersection with the parabola.

Medium
< 1min
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Outcomes

10.CG.L.1

Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of geometrical representation of quadratic polynomials. Distance between two points and section formula (internal). Area of a triangle.

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