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Home Question Bank Math Geometry Archive 2025 January 04

Geometry Questions from Jan 04,2025

Browse the Geometry Q&A Archive for Jan 04,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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17 Точка \( P \) лежит на стороне \( A C \) равностороннего треугольника \( A B C \). Окружность с диа- метром \( B P \) пересекает стороны \( A B \) и \( B C \) в точках \( M \) и \( N \) соответственно. Хорды \( M F \) и \( N E \) параллельны прямой \( B P \). Отрезки \( F P \) и \( E P \) пересекают стороны \( A B \) и \( B C \) в точках \( T \) и \( S \) соответственно. а) Докажите, что треугольники \( A P T \) и \( C S P \) подобны. б) Найдите отношение, в котором точка \( P \) делит отрезок \( A C \), если площади треугольни- ков \( A P T \) и \( C S P \) относятся как \( 49: 121 \). Partie \( A: \) Sur la figure ci-dessous. fes points \( A, B \) et \( E \) sont alignés, et \( C \) est le midieu du segment \( [F B] \). \( A B=40 \mathrm{~m}, A C=50 \mathrm{~cm}, B E=70 \mathrm{~m} \) et \( B C=30 \mathrm{~m} \) 1. Montre que \( A B C \) est un triangle rectangle en \( B \). 2. Calcule la valeur exacte de \( E F \), puis arrondis te résuttat au dixième Près (un chiffre après la virgule). 22 If right triattgle \( A B C \) has sides \( b=7 \) and \( c=24 \), then which of the follarwing is a possible value for the perimeter of triangle \( A B C \) ? A) 50 B) 25 C) 56 D) 84 What conic section is represented by the equation \( 3 x^{2}+2 y^{2}-24 x+30=0 \) ? Explain. (4 points) B \( I \) U Is the ellipse represented by the equation \( \frac{(x-5)^{2}}{3}+\frac{(y+1)^{2}}{5}=1 \) oriented horizontally or vertically? Explain how you know. (4 points) B \( I \) \( \underline{\mathrm{u}} \) Write the equation of the hyperbola with center \( (2,-5) \), vertex \( (2,-2) \), and focus \( (2,-5+2 \sqrt{3}) \) (1 point) (y+5)\( \frac{\frac{(y+5)^{2}}{9}-\frac{(x-2)^{2}}{3}=1}{\frac{(y+5)^{2}}{3}-\frac{(x-2)^{2}}{9}=1} \) \( \frac{(y+5)^{2}}{12}-\frac{(x-2)^{2}}{9}=1 \) A parabolic microphone used on the sidelines of a professional football game uses a reflective dish 16 in. wide and 4 in . deep. How far from the bottom of the dish should the microphone be placed? (1 point) 3 in . 3.2 in . 3.8 in . 4 in . Identify the focus and directrix of the parabola whose equation is \( (y-3)^{2}=-4(x-5) \). (1 point) focus: \( (4,2) \); directrix: \( y=4 \) focus: \( (4,4) \); directrix: \( y=2 \) focus: \( (4,3) \); directrix: \( x=6 \) focus: \( (6,3) \); directrix: \( x=4 \) The equation of an ellipse is \( 4 x^{2}+y^{2}+10 y+13=0 \). Write the equation in standard form. (1 point) \( 0 \frac{x^{2}}{4}+\frac{(y+5)^{2}}{3}=1 \) \( 0 \frac{x^{2}}{3}+\frac{(y+5)^{2}}{12}=1 \) \( 0 \frac{x^{2}}{12}+\frac{(y+5)^{2}}{3}=1 \) The equation that models Pluto's elliptical orbit around the sun is \( \frac{(x+0.9)^{2}}{12.96}+\frac{y^{2}}{12.15}=1 \) in billions of miles. If the sun is located at one focus and its coordinates are \( (0,0) \), find Pluto's farthest distance from the sun in billions of miles. (1 point) 13.86 billion mi . 12.06 billion mi . 4.50 billion mi. 2.70 billion mi.
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