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Sia ? 6 years, 4 months ago
The distance of the point (h, k) from x-axis i.e. distance between (h,k) and (x,0) is
{tex}Distance=\sqrt{(x-h)^2 +(0-k)^2}{/tex} [By using distance formula]
{tex}\Rightarrow Distance=\sqrt{x^2+h^2-2xh+k^2}{/tex}
{tex}\Rightarrow Distance=\sqrt{x^2+h^2+k^2-2xh}{/tex}
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Yogita Ingle 7 years, 3 months ago
p(x) = 4x² - 4x - 3
⇒ 4x² - 6x + 2x - 3
⇒ 2x( 2x -3) + 1(2x + 3)
⇒ (2x + 1) (2x -3)
p(x) = 0
(2x + 1) = 0 or (2x-3) = 0
x = -1/2 or x = 3/2
Hence, -1/2 and 3/2 are the zeroes of p(x).
Sum of zeroes = -1/2 + 3/2 = 2/2 = 1 = Coefficient of x / Coefficient of x²
Product of zeroes = (-1/2)(3/2) = -3/4 = Constant term/ Coefficient of x²
Posted by Deepak Jha 6 years, 4 months ago
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Sia ? 6 years, 4 months ago
Let PQ and RS be two parallel tangents of a circle where centre is O. Let their points of contact be A and B respectively. Join OA and OB.
Draw OC {tex}\parallel{/tex} PQ or RS
Now PQ {tex}\parallel{/tex} OC and transversal AO intersects them
{tex}\therefore{/tex} {tex}\angle{/tex}PAO + {tex}\angle{/tex}COA = 180o [{tex}\because{/tex} The sum of consecutive interior angles on the same side of the transverse is 180o]
⇒ 90°+ {tex}\angle{/tex}COA = 180o [{tex}\because{/tex} PA is a tangent and OA is the radius through the point of contact]
{tex}\therefore{/tex} {tex}\angle{/tex}PAO = 90o [ the tangent of any point of a circle is perpendicular to the radius through the property contact]
{tex}\Rightarrow{/tex} {tex}\angle{/tex}COA = 90o
Similarly,
{tex}\angle{/tex}COB = 90o
{tex}\therefore{/tex} {tex}\angle{/tex}COA + {tex}\angle{/tex}COB = 180o
{tex}\Rightarrow{/tex} AB is a straight line through O.
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