Perpendicular gradients, medians, the equation of a circle, tangents and the discriminant test for tangency — every coordinate given, no diagram needed…
10 questions • Zestly
• A straight line has a gradient of $\frac{2}{5}$. What is the gradient of any line perpendicular to it?
• A straight line makes an angle of $60^{\circ}$ with the positive direction of the x-axis. What is its gradient?
• What is the equation of the line passing through the point $(2, -1)$ and perpendicular to the line $y = 2x + 7$?
• A circle has centre $(-2, 5)$ and radius $3$. What is its equation?
• A circle has the equation $x^2 + y^2 - 6x + 4y - 12 = 0$. What are its centre and radius?
• Does the point $(6, 1)$ lie inside, on, or outside the circle $(x - 2)^2 + (y + 1)^2 = 25$?
• A circle has centre $(1, 3)$, and a tangent touches it at the point $(4, 7)$. What is the gradient of that tangent?
• What is the midpoint of the line joining $A(-3, 8)$ and $B(5, -2)$?
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